%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM080_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 : n016.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 71.14s 43.33s
% Output : Refutation 63.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 123
% Syntax : Number of formulae : 248 ( 101 unt; 0 typ; 0 def)
% Number of atoms : 1024 ( 271 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 4977 ( 45 ~; 11 |; 63 &;4639 @)
% ( 24 <=>; 195 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 13 con; 0-5 aty)
% Number of variables : 617 ( 0 ^; 603 !; 14 ?; 617 :)
% 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(cl_Groups_Oplus_decl,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
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 ) ) > ( TA @ list @ ( TB @ list @ fun ) @ ( TC @ list @ fun ) ) ) ).
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_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(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(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(map_fm_decl,type,
map_fm:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ fm ) > ( TA @ fm ) ) ).
thf(neg_decl,type,
neg:
!>[TA: $tType] : ( ( TA @ fm ) > ( TA @ fm ) ) ).
thf(qfree_decl,type,
qfree:
!>[TA: $tType] : ( ( TA @ fm ) > $o ) ).
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 @ fun ) ) ).
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(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(il_decl,type,
il: int ).
thf(ksl_decl,type,
ksl: int @ list ).
thf(m_decl,type,
m: int ).
thf(xs_decl,type,
xs: int @ list ).
thf(1,conjecture,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( xs @ ( ksl @ ( int @ iprod ) ) @ ( m @ ( il @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( A @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( xs @ ( ksl @ ( int @ iprod ) ) @ ( m @ ( il @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( A @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(125,plain,
~ ! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( xs @ ( ksl @ ( int @ iprod ) ) @ ( m @ ( il @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( A @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(249,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(64,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insert__Nil) ).
thf(352,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero @ suc ) )
<=> ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult__eq__1__iff) ).
thf(170,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero @ suc ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero @ suc ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero @ suc ) )
=> ( ( A
= ( nat @ zero_zero @ suc ) )
& ( B
= ( nat @ zero_zero @ suc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,axiom,
int @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(523,plain,
int @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_68_in__set__sublistD) ).
thf(247,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)],[33]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_list__ex1__simps_I1_J) ).
thf(202,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(112,axiom,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( ksl @ ( m @ ( il @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).
thf(533,plain,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( ksl @ ( m @ ( il @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_iprod__Nil) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(538,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(15,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(185,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__cancel) ).
thf(417,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__Cons__self) ).
thf(288,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(121,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(565,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(119,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_set__ConsD) ).
thf(559,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_divisor__asubst) ).
thf(325,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_splice__Nil2) ).
thf(152,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(90,axiom,
! [A: int @ list,B: int @ list,C: int,D: atom @ fm] :
( ( D @ ( atom @ qfree ) )
=> ( ( A @ ( A @ ( B @ ( int @ iprod ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( D @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
<=> ( A @ ( D @ ( B @ ( C @ asubst ) @ ( atom @ ( atom @ map_fm ) ) ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_I__subst) ).
thf(448,plain,
! [A: int @ list,B: int @ list,C: int,D: atom @ fm] :
( ( D @ ( atom @ qfree ) )
=> ( ( ( A @ ( D @ ( B @ ( C @ asubst ) @ ( atom @ ( atom @ map_fm ) ) ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
=> ( A @ ( A @ ( B @ ( int @ iprod ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( D @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) )
& ( ( A @ ( A @ ( B @ ( int @ iprod ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( D @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) )
=> ( A @ ( D @ ( B @ ( C @ asubst ) @ ( atom @ ( atom @ map_fm ) ) ) @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__add__commute) ).
thf(316,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_splice_Osimps_I1_J) ).
thf(164,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,axiom,
! [TA: $tType,A: TA @ fm @ list] :
( ! [B: TA @ fm] :
( ( A @ ( TA @ fm @ set ) @ ( B @ ( TA @ fm @ member ) ) )
=> ( B @ ( TA @ qfree ) ) )
=> ( A @ ( TA @ list_conj ) @ ( TA @ qfree ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_qfree__list__conj) ).
thf(348,plain,
! [TA: $tType,A: TA @ fm @ list] :
( ! [B: TA @ fm] :
( ( A @ ( TA @ fm @ set ) @ ( B @ ( TA @ fm @ member ) ) )
=> ( B @ ( TA @ qfree ) ) )
=> ( A @ ( TA @ list_conj ) @ ( TA @ qfree ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_52_Z_OI__list__disj) ).
thf(396,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)],[74]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list__add__Cons) ).
thf(243,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_add__0__right) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zipwith0_Osimps_I3_J) ).
thf(265,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_mult__Suc__right) ).
thf(527,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_in__set__insert) ).
thf(307,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)],[51]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_mult__Suc) ).
thf(292,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_list__add__Nil2) ).
thf(512,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_add__imp__eq) ).
thf(366,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add_Ocomm__neutral) ).
thf(233,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(91,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_not__in__set__insert) ).
thf(452,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(48,axiom,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(297,plain,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add__left__cancel) ).
thf(275,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(95,axiom,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( A @ ( B @ ( C @ ( D @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp )
<=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_IZ__asubst) ).
thf(467,plain,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( D @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp )
=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_double__zero__sym) ).
thf(566,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_iprod__Cons) ).
thf(252,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(197,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_34_iprod0__if__coeffs0) ).
thf(435,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)],[85]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_List_Oinsert__def) ).
thf(461,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(42,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 @ list @ ( TC @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ list @ ( TC @ list @ aa ) ) ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_zipwith0_Osimps_I1_J) ).
thf(285,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 @ list @ ( TC @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ list @ ( TC @ list @ aa ) ) ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zero__reorient) ).
thf(156,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)],[9]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(403,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(66,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_75_mem__def) ).
thf(356,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)],[66]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
<=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__cancel1) ).
thf(141,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_iprod__left__add__distrib) ).
thf(499,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_35_Z_OI__list__conj) ).
thf(328,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)],[57]) ).
thf(59,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(339,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__0__iff) ).
thf(489,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(24,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mult__0__right) ).
thf(212,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_nat__add__right__cancel) ).
thf(515,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat_Oinject) ).
thf(129,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)],[3]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_not__Cons__self2) ).
thf(343,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(67,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( 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(360,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(21,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_55_list_Osimps_I4_J) ).
thf(205,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)],[21]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(541,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(111,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list_Osimps_I3_J) ).
thf(530,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_67_notin__set__sublistI) ).
thf(412,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)],[78]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__0) ).
thf(425,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(123,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_56_list_Osimps_I5_J) ).
thf(573,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)],[123]) ).
thf(88,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(444,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,axiom,
nat @ cl_Groups_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oplus) ).
thf(180,plain,
nat @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(47,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(296,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(562,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(44,axiom,
int @ cl_Groups_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(291,plain,
int @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(20,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(204,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__add__left__commute) ).
thf(445,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__right__cancel) ).
thf(236,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA @ fm,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ map_fm ) ) ) @ ( TB @ qfree ) )
<=> ( A @ ( TA @ qfree ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_qfree__map__fm) ).
thf(181,plain,
! [TA: $tType,TB: $tType,A: TA @ fm,B: TB @ ( TA @ fun )] :
( ( ( A @ ( TA @ qfree ) )
=> ( A @ ( B @ ( TB @ ( TA @ map_fm ) ) ) @ ( TB @ qfree ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ map_fm ) ) ) @ ( TB @ qfree ) )
=> ( A @ ( TA @ qfree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__left__imp__eq) ).
thf(406,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__cancel2) ).
thf(219,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,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_54_splice_Osimps_I2_J) ).
thf(230,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)],[28]) ).
thf(105,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_36_list_Oexhaust) ).
thf(509,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)],[105]) ).
thf(22,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(208,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(97,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_6_list_Oinject) ).
thf(477,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)],[97]) ).
thf(117,axiom,
~ ! [A: int,B: int @ list,C: int] :
~ ! [D: atom] :
( ( as @ ( atom @ set ) @ ( D @ ( atom @ member ) ) )
=> ( xs @ ( D @ ( B @ ( C @ ( A @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_B_Bthesis_O_A_I_B_Bil_Aksl_Am_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(552,plain,
~ ! [A: int,B: int @ list,C: int] :
~ ! [D: atom] :
( ( as @ ( atom @ set ) @ ( D @ ( atom @ member ) ) )
=> ( xs @ ( D @ ( B @ ( C @ ( A @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ asubst ) @ ( atom @ ( atom @ aa ) ) ) @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(113,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat_Oadd__0__right) ).
thf(535,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(5,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(140,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(155,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [TA: $tType,A: TA @ fm] :
( ( A @ ( TA @ neg ) @ ( TA @ qfree ) )
<=> ( A @ ( TA @ qfree ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_qfree__neg) ).
thf(198,plain,
! [TA: $tType,A: TA @ fm] :
( ( ( A @ ( TA @ qfree ) )
=> ( A @ ( TA @ neg ) @ ( TA @ qfree ) ) )
& ( ( A @ ( TA @ neg ) @ ( TA @ qfree ) )
=> ( A @ ( TA @ qfree ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(455,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(103,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(505,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(83,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(431,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(11,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult__0) ).
thf(167,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__eq__self__zero) ).
thf(473,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(36,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_37_neq__Nil__conv) ).
thf(255,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)],[36]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_sublist__nil) ).
thf(209,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(355,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(458,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(46,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(295,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add__right__imp__eq) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_iprod__Nil2) ).
thf(414,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__Suc) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(52,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_64_sublist__singleton) ).
thf(310,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)],[52]) ).
thf(86,axiom,
xs @ ( as @ qEpres896714165pres_1 @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096) ).
thf(441,plain,
xs @ ( as @ qEpres896714165pres_1 @ ( i_Z @ ( int @ ( atom @ interpret ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(370,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)],[71]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__0__left) ).
thf(502,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_list__add__assoc) ).
thf(576,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(116,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(544,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)],[116]) ).
thf(58,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list_Osimps_I2_J) ).
thf(336,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__is__0) ).
thf(386,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(109,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( C @ ( TA @ list_size ) ) @ ( B @ ( C @ ( nat @ ( TA @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_list_Osize_I2_J) ).
thf(524,plain,
! [TA: $tType,A: TA @ list,B: TA,C: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_size ) ) )
= ( nat @ zero_zero @ suc @ ( A @ ( C @ ( TA @ list_size ) ) @ ( B @ ( C @ ( nat @ ( TA @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(26,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(218,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(68,axiom,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_norm) ).
thf(363,plain,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__add__Nil) ).
thf(556,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(54,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_zipwith0_Osimps_I2_J) ).
thf(319,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(50,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_57_splice_Osimps_I3_J) ).
thf(304,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)],[50]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mult__is__0) ).
thf(186,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(139,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(246,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(346,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ fm @ list] :
( ! [B: TA @ fm] :
( ( A @ ( TA @ fm @ set ) @ ( B @ ( TA @ fm @ member ) ) )
=> ( B @ ( TA @ qfree ) ) )
=> ( A @ ( TA @ list_disj ) @ ( TA @ qfree ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_qfree__list__disj) ).
thf(300,plain,
! [TA: $tType,A: TA @ fm @ list] :
( ! [B: TA @ fm] :
( ( A @ ( TA @ fm @ set ) @ ( B @ ( TA @ fm @ member ) ) )
=> ( B @ ( TA @ qfree ) ) )
=> ( A @ ( TA @ list_disj ) @ ( TA @ qfree ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(432,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list__add__def) ).
thf(262,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_69_list__ex1__iff) ).
thf(373,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)],[72]) ).
thf(104,axiom,
( ( ( as @ lbounds )
= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_calculation) ).
thf(506,plain,
( ( ( as @ lbounds )
= ( int @ list @ ( int @ product_prod ) @ nil ) )
=> ? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ ( i_Z @ ( bool @ ( int @ list @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( int @ list @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_double__eq__0__iff) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(442,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(70,axiom,
int @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(369,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__assoc) ).
thf(322,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( C @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(98,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_plus__nat_Oadd__0) ).
thf(486,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(25,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_list_Osize_I1_J) ).
thf(215,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(100,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2560,plain,
$false,
inference(e,[status(thm)],[125,249,352,170,523,247,202,533,340,538,185,417,288,565,559,325,152,448,316,164,348,396,243,428,265,527,307,292,512,366,233,452,297,275,467,566,252,197,435,461,285,156,403,356,141,499,328,339,489,212,515,129,343,360,205,541,530,412,425,573,444,180,296,562,291,204,445,236,181,406,219,230,509,208,477,552,535,140,155,198,455,505,431,167,473,255,209,355,458,295,282,414,409,310,441,370,502,576,544,336,386,524,218,363,556,319,304,186,139,246,346,300,432,262,373,506,268,442,369,322,486,215,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM080_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/15.43 % Computer : n016.cluster.edu
% 0.13/15.43 % Model : x86_64 x86_64
% 0.13/15.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.43 % Memory : 8046.5625MB
% 0.13/15.43 % OS : Linux 6.8.0-71-generic
% 0.13/15.43 % CPULimit : 300
% 0.13/15.43 % WCLimit : 300
% 0.13/15.43 % DateTime : Sat Sep 26 23:32:46 UTC 2026
% 0.13/15.43 % CPUTime :
% 0.13/15.43 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
% 0.18/16.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/16.32 % [INFO] Parsing done (305ms).
% 1.81/16.33 % [INFO] Running in sequential loop mode.
% 2.61/16.72 % [INFO] eprover registered as external prover.
% 2.61/16.73 % [INFO] Scanning for conjecture ...
% 2.98/16.92 % [INFO] Found a conjecture (or negated_conjecture) and 122 axioms. Running axiom selection ...
% 3.35/17.08 % [INFO] Axiom selection finished. Selected 122 axioms (removed 0 axioms).
% 4.22/17.30 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.22/17.33 % [INFO] Type checking passed.
% 4.22/17.33 % [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 ...
% 71.14/43.32 % External prover 'e' found a proof!
% 71.14/43.32 % [INFO] Killing All external provers ...
% 71.14/43.32 % Time passed: 27751ms (effective reasoning time: 26984ms)
% 71.14/43.32 % 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)>
% 71.14/43.33 % Axioms used in derivation (122): arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_18_zero__reorient, fact_56_list_Osimps_I5_J, fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096, fact_72_qfree__list__conj, fact_53_insert__Nil, fact_43_zipwith0_Osimps_I1_J, fact_86_list__nonempty__induct, fact_66_sublist__nil, fact_7_add__left__cancel, fact_6_list_Oinject, fact_39_zipwith0_Osimps_I3_J, fact_73_nat__add__right__cancel, fact_4_IZ__asubst, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_79_nat__add__commute, fact_40_add__0__iff, fact_54_splice_Osimps_I2_J, fact_5__096lbounds_Aas_A_126_061_A_091_093_096, fact_97_add__Suc, fact_71_qfree__map__fm, fact_75_mem__def, arity_Int_Oint___Rings_Oring, fact_42_zipwith0_Osimps_I2_J, fact_52_Z_OI__list__disj, fact_29_add__left__imp__eq, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_93_mult__0, fact_10_calculation, fact_68_in__set__sublistD, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, arity_Nat_Onat___Groups_Oplus, fact_16_iprod__Nil, fact_32_not__Cons__self, fact_1__096_B_Bthesis_O_A_I_B_Bil_Aksl_Am_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_77_nat__add__assoc, arity_Int_Oint___Groups_Oplus, fact_25_add__0, fact_74_ext, fact_96_mult__Suc, fact_34_iprod0__if__coeffs0, fact_88_iprod__Cons, fact_87_list_Osize_I2_J, fact_64_sublist__singleton, fact_95_mult__eq__1__iff, fact_20_list__add__assoc, fact_89_mult__cancel2, fact_92_mult__0__right, fact_58_in__set__insert, arity_List_Olist___Groups_Oplus, fact_19_list__add__Nil2, fact_27_add__right__imp__eq, fact_98_mult__Suc__right, fact_33_double__eq__0__iff, fact_50_list__add__def, fact_8_add__right__cancel, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_67_notin__set__sublistI, fact_12_norm, fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_81_Nat_Oadd__0__right, arity_Nat_Onat___Groups_Ozero, fact_17_list__add__Nil, fact_9_iprod__left__add__distrib, arity_Int_Oint___Groups_Omonoid__add, fact_21_list_Osimps_I3_J, fact_94_nat_Oinject, fact_78_nat__add__left__commute, fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_62_List_Oinsert__def, fact_36_list_Oexhaust, fact_37_neq__Nil__conv, fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_65_I__subst, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_83_qfree__list__disj, fact_3_list__add__Cons, fact_2__096Z_OI_A_Iqe__pres_092_060_094isub_0621_Aas_J_Axs_096, fact_80_plus__nat_Oadd__0, fact_14_divisor__asubst, fact_35_Z_OI__list__conj, fact_11_set__ConsD, fact_61_not__in__set__insert, fact_57_splice_Osimps_I3_J, fact_24_add__0__right, fact_82_add__eq__self__zero, fact_69_list__ex1__iff, arity_Int_Oint___Groups_Oab__semigroup__add, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_60_splice__Nil2, fact_55_list_Osimps_I4_J, fact_84_qfree__neg, help_pp_1_1_U, fact_76_nat__add__left__cancel, fact_59_splice_Osimps_I1_J, fact_70_add__is__0, fact_31_not__Cons__self2, arity_Nat_Onat___Groups_Omonoid__add, fact_23_add_Ocomm__neutral, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, help_pp_2_1_U, fact_26_add__0__left, fact_15_iprod__Nil2, fact_90_mult__cancel1, fact_30_ab__semigroup__add__class_Oadd__ac_I1_J, fact_63_list__ex1__simps_I1_J, fact_38_zipwith0_Osimps_I4_J, fact_13_double__zero__sym, fact_91_mult__is__0, fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_28_add__imp__eq, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_85_list_Osize_I1_J, fact_22_list_Osimps_I2_J
% 71.14/43.33 % No. of inferences in proof: 248
% 71.14/43.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 27751 ms resp. 26984 ms w/o parsing
% 63.47/43.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.47/43.45 % [INFO] Killing All external provers ...
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