TSTP Solution File: COM041_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM041_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:13:58 EDT 2023
% Result : Theorem 14.79s 6.04s
% Output : Refutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 171
% Syntax : Number of formulae : 295 ( 86 unt; 49 typ; 0 def)
% Number of atoms : 913 ( 283 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 6190 ( 23 ~; 3 |; 45 &;5919 @)
% ( 12 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 11 con; 0-5 aty)
% Number of variables : 805 ( 0 ^; 770 !; 0 ?; 805 :)
% ( 35 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_type,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_type,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(semiring_type,type,
semiring:
!>[TA: $tType] : $o ).
thf(comm_ring_type,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_type,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(semiring_div_type,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_type,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(div_mod_type,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > ( fun @ TA @ TA ) ) ).
thf(iprod_type,type,
iprod:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > TA ) ).
thf(zipwith0_type,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ ( list @ TC ) @ ( fun @ ( list @ TB ) @ ( list @ TA ) ) ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(i_Z_type,type,
i_Z: atom > ( list @ int ) > $o ).
thf(asubst_type,type,
asubst: int > ( list @ int ) > atom > atom ).
thf(dvd_type,type,
dvd: int > int > ( list @ int ) > atom ).
thf(c_PresArith_Oatom_OLe_type,type,
c_PresArith_Oatom_OLe: int > ( list @ int ) > atom ).
thf(nDvd_type,type,
nDvd: int > int > ( list @ int ) > atom ).
thf(atom_case_type,type,
atom_case:
!>[TA: $tType] : ( ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > atom > TA ) ).
thf(atom_rec_type,type,
atom_rec:
!>[TA: $tType] : ( ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > atom > TA ) ).
thf(divisor_type,type,
divisor: atom > int ).
thf(hd_coeff_type,type,
hd_coeff: atom > int ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(a_type,type,
a: atom ).
thf(d_type,type,
d: int ).
thf(e_type,type,
e: list @ int ).
thf(i_type,type,
i: int ).
thf(j_type,type,
j: int ).
thf(ks_type,type,
ks: list @ int ).
thf(ks1_type,type,
ks1: list @ int ).
thf(l_type,type,
l: int ).
thf(6,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(141,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,axiom,
semiring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(352,plain,
semiring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(61,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_mult__left__idem) ).
thf(333,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(34,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(249,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
( a
= ( nDvd @ d @ l @ ks1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_NDvd) ).
thf(217,plain,
( a
= ( nDvd @ d @ l @ ks1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_atom_Osimps_I12_J) ).
thf(379,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(80,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(385,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zmod__simps_I2_J) ).
thf(500,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( minus_minus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( minus_minus @ TA @ D @ B ) @ ( minus_minus @ ( list @ TA ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list__diff__Cons__Cons) ).
thf(174,plain,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( minus_minus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( minus_minus @ TA @ D @ B ) @ ( minus_minus @ ( list @ TA ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(98,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
thf(436,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(82,axiom,
comm_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
thf(389,plain,
comm_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_not__Cons__self) ).
thf(184,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(75,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(372,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(71,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_mod__mult__eq) ).
thf(357,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(91,axiom,
! [A: list @ int,B: int] :
( ( divisor @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_divisor_Osimps_I1_J) ).
thf(416,plain,
! [A: list @ int,B: int] :
( ( divisor @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(325,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(48,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(289,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
cl_Groups_Ominus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(216,plain,
cl_Groups_Ominus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: TA] :
( ( iprod @ TA @ ( map @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( iprod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_iprod__assoc) ).
thf(376,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: TA] :
( ( iprod @ TA @ ( map @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( iprod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_list__add__Cons) ).
thf(211,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ B )
= ( div_mod @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mod__mult__self2) ).
thf(485,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ B )
= ( div_mod @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(29,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(238,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(66,axiom,
ab_semigroup_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(348,plain,
ab_semigroup_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(69,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(353,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(9,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_atom_Osimps_I2_J) ).
thf(147,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( iprod @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( iprod @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_iprod__Cons) ).
thf(280,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( iprod @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( iprod @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(50,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(293,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(103,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(453,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(32,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_mult__1) ).
thf(243,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(428,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(40,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_times_Oidem) ).
thf(265,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
! [A: list @ int,B: atom,C: list @ int,D: int] :
( ( i_Z @ ( asubst @ D @ C @ B ) @ A )
<=> ( i_Z @ B @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_IZ__asubst) ).
thf(233,plain,
! [A: list @ int,B: atom,C: list @ int,D: int] :
( ( ( i_Z @ ( asubst @ D @ C @ B ) @ A )
=> ( i_Z @ B @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) ) )
& ( ( i_Z @ B @ ( cons @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ D ) @ ( iprod @ int @ C @ A ) ) @ A ) )
=> ( i_Z @ ( asubst @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ( ( plus_plus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( plus_plus @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list__add__def) ).
thf(439,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ( ( plus_plus @ ( list @ TA ) )
= ( zipwith0 @ TA @ TA @ TA @ ( plus_plus @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(24,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list__add__assoc) ).
thf(220,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(67,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_mod__mult__left__eq) ).
thf(349,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(84,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(392,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(52,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( D != C )
& ( B != A ) )
<=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
!= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_crossproduct__noteq) ).
thf(297,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( D != C )
& ( B != A ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
!= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) ) )
& ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
!= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(88,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zmod__zmult1__eq) ).
thf(407,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(5,axiom,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( nDvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atom_Osimps_I7_J) ).
thf(137,plain,
! [A: list @ int,B: int,C: list @ int,D: int,E: int] :
( ( nDvd @ E @ D @ C )
!= ( c_PresArith_Oatom_OLe @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_map_Osimps_I2_J) ).
thf(467,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(35,axiom,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_atom_Orecs_I1_J) ).
thf(252,plain,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_atom_Osimps_I3_J) ).
thf(197,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( nDvd @ F @ E @ D )
= ( nDvd @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(107,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mult__1__left) ).
thf(461,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(37,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(256,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(115,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(488,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1,conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ l ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) ) @ d )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( div_mod @ int @ l @ d ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) @ d ) ) @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ l ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) ) @ d )
!= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( div_mod @ int @ l @ d ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) @ d ) ) @ d ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(124,plain,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ l ) @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) ) @ d )
!= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( div_mod @ int @ l @ d ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ i ) @ ( iprod @ int @ ks @ e ) ) @ d ) ) @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(339,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) )
<=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ E @ B ) ) @ D ) ) @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_eq__add__iff1) ).
thf(476,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ E @ B ) ) @ D ) ) @ C )
= A ) )
& ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ E @ B ) ) @ D ) ) @ C )
= A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(105,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(457,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(120,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__add__cong) ).
thf(503,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(4,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__Cons__self2) ).
thf(134,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( iprod @ TA @ C @ A ) ) @ ( iprod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_iprod__left__add__distrib) ).
thf(360,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( plus_plus @ ( list @ TA ) ) @ C ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( iprod @ TA @ C @ A ) ) @ ( iprod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(86,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_mult_Ocomm__neutral) ).
thf(398,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(94,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) @ ( minus_minus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_square__diff__square__factored) ).
thf(425,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) ) @ ( minus_minus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(10,axiom,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_atom_Osimps_I1_J) ).
thf(161,plain,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_PresArith_Oatom_OLe @ D @ C )
= ( c_PresArith_Oatom_OLe @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(286,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(259,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(90,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(413,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(101,axiom,
~ ! [A: list @ int] :
( ks1
!= ( cons @ int @ ( one_one @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__096_B_Bthesis_O_A_I_B_Bks_H_O_Aks_A_061_A1_A_D_Aks_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(445,plain,
~ ! [A: list @ int] :
( ks1
!= ( cons @ int @ ( one_one @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(79,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zmod__simps_I4_J) ).
thf(382,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(8,axiom,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( asubst @ C @ B @ A ) )
= ( divisor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_divisor__asubst) ).
thf(144,plain,
! [A: atom,B: list @ int,C: int] :
( ( divisor @ ( asubst @ C @ B @ A ) )
= ( divisor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: list @ TA] :
( ( map @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_scale1) ).
thf(181,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: list @ TA] :
( ( map @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( nDvd @ C @ B @ A ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_divisor_Osimps_I3_J) ).
thf(187,plain,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( nDvd @ C @ B @ A ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(172,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
comm_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(219,plain,
comm_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(43,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(274,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(92,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( one_one @ TA ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(419,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( one_one @ TA ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(122,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(509,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(42,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_mod__add__eq) ).
thf(271,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(117,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mod__mult__mult1) ).
thf(494,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(65,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(345,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mod__mult__mult2) ).
thf(330,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(25,axiom,
! [A: list @ int,B: int,C: int,D: int,E: list @ int,F: int] :
( ( asubst @ F @ E @ ( nDvd @ D @ C @ ( cons @ int @ B @ A ) ) )
= ( nDvd @ D @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( aa @ int @ int @ ( times_times @ int @ B ) @ F ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_asubst_Osimps_I3_J) ).
thf(223,plain,
! [A: list @ int,B: int,C: int,D: int,E: list @ int,F: int] :
( ( asubst @ F @ E @ ( nDvd @ D @ C @ ( cons @ int @ B @ A ) ) )
= ( nDvd @ D @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( aa @ int @ int @ ( times_times @ int @ B ) @ F ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(306,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(26,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__left__cancel) ).
thf(226,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(96,axiom,
( ks1
= ( cons @ int @ ( one_one @ int ) @ ks ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__096ks_A_061_A1_A_D_Aks_H_096) ).
thf(431,plain,
( ks1
= ( cons @ int @ ( one_one @ int ) @ ks ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(473,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(36,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(255,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(64,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zmod__simps_I1_J) ).
thf(342,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_mod__add__self1) ).
thf(458,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(59,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zmod__simps_I3_J) ).
thf(327,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(55,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_crossproduct__eq) ).
thf(310,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_atom_Osimps_I6_J) ).
thf(177,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( c_PresArith_Oatom_OLe @ E @ D )
!= ( nDvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mod__mult__cong) ).
thf(470,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(62,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(336,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(81,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(386,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(7,axiom,
cl_Groups_Ominus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(143,plain,
cl_Groups_Ominus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(118,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(497,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( one_one @ TA ) ) @ ( one_one @ TA ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(102,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__1__right) ).
thf(450,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(73,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__right__cancel) ).
thf(363,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(113,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__idem) ).
thf(482,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(56,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( div_mod @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mod__mult__self1) ).
thf(319,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( div_mod @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(83,axiom,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_assms_I2_J) ).
thf(390,plain,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(87,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) )
<=> ( C
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ B @ E ) ) @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_eq__add__iff2) ).
thf(401,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) )
=> ( C
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ B @ E ) ) @ D ) ) @ A ) ) )
& ( ( C
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( minus_minus @ TA @ B @ E ) ) @ D ) ) @ A ) )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ E ) @ D ) ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ D ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(49,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( one_one @ TA ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(290,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ ( one_one @ TA ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(33,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(246,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,axiom,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms_I3_J) ).
thf(214,plain,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: list @ TC,D: TC,E: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ ( cons @ TC @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ E @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zipwith0_Osimps_I2_J) ).
thf(433,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( zero @ TA )
& ( zero @ TC ) )
=> ! [A: list @ TA,B: TA,C: list @ TC,D: TC,E: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ ( cons @ TC @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ E @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TB ) @ ( aa @ ( list @ TC ) @ ( fun @ ( list @ TA ) @ ( list @ TB ) ) @ ( zipwith0 @ TC @ TA @ TB @ E ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(123,axiom,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_combine__common__factor) ).
thf(510,plain,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ D ) @ C ) ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ D ) @ B ) ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(89,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_mod__mult__right__eq) ).
thf(410,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(39,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mod__add__left__eq) ).
thf(262,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(17,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_one__reorient) ).
thf(190,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(93,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
thf(422,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(76,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(373,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(46,axiom,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_atom_Osimps_I10_J) ).
thf(283,plain,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_case @ TA @ E @ D @ C @ ( c_PresArith_Oatom_OLe @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( asubst @ E @ D @ ( c_PresArith_Oatom_OLe @ C @ ( cons @ int @ B @ A ) ) )
= ( c_PresArith_Oatom_OLe @ ( minus_minus @ int @ C @ ( aa @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_asubst_Osimps_I1_J) ).
thf(239,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int] :
( ( asubst @ E @ D @ ( c_PresArith_Oatom_OLe @ C @ ( cons @ int @ B @ A ) ) )
= ( c_PresArith_Oatom_OLe @ ( minus_minus @ int @ C @ ( aa @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(31,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(242,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(51,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
thf(294,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list_Oinject) ).
thf(126,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(506,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(41,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(268,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(85,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(395,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(108,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(464,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(44,axiom,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_atom_Orecs_I3_J) ).
thf(277,plain,
! [TA: $tType,A: list @ int,B: int,C: int,D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),F: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( atom_rec @ TA @ F @ E @ D @ ( nDvd @ C @ B @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ ( aa @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(100,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_mod__mod__trivial) ).
thf(442,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(74,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_mod__add__right__eq) ).
thf(369,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(57,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(322,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(70,axiom,
! [A: list @ int,B: int,C: int,D: int,E: list @ int,F: int] :
( ( asubst @ F @ E @ ( dvd @ D @ C @ ( cons @ int @ B @ A ) ) )
= ( dvd @ D @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( aa @ int @ int @ ( times_times @ int @ B ) @ F ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I2_J) ).
thf(354,plain,
! [A: list @ int,B: int,C: int,D: int,E: list @ int,F: int] :
( ( asubst @ F @ E @ ( dvd @ D @ C @ ( cons @ int @ B @ A ) ) )
= ( dvd @ D @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ C ) @ ( aa @ int @ int @ ( times_times @ int @ B ) @ F ) ) @ ( aa @ ( list @ int ) @ ( list @ int ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( plus_plus @ ( list @ int ) ) @ ( map @ int @ int @ ( times_times @ int @ B ) @ E ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(54,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(309,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(116,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_mod__add__self2) ).
thf(491,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ B ) @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(104,axiom,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comm__semiring__class_Odistrib) ).
thf(454,plain,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( plus_plus @ TA ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(27,axiom,
cl_Groups_Oplus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(232,plain,
cl_Groups_Oplus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(513,plain,
$false,
inference(e,[status(thm)],[141,352,333,249,217,379,385,500,174,436,389,184,372,357,416,325,289,216,376,211,485,238,348,353,147,280,293,453,243,428,265,233,439,220,349,392,297,407,137,467,252,197,461,256,488,124,339,476,457,503,134,360,398,425,161,286,259,413,445,382,144,181,187,172,219,274,419,509,271,494,345,330,223,306,226,431,473,255,342,458,327,310,177,470,336,386,143,497,450,363,482,319,390,401,290,246,214,433,510,410,262,190,422,373,283,239,242,294,126,506,268,395,464,277,442,369,322,354,309,491,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM041_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:17:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.85/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.02 % [INFO] Parsing done (199ms).
% 1.56/1.03 % [INFO] Running in sequential loop mode.
% 2.24/1.23 % [INFO] eprover registered as external prover.
% 2.24/1.23 % [INFO] cvc4 registered as external prover.
% 2.24/1.24 % [INFO] Scanning for conjecture ...
% 2.52/1.34 % [INFO] Found a conjecture and 123 axioms. Running axiom selection ...
% 2.77/1.41 % [INFO] Axiom selection finished. Selected 121 axioms (removed 2 axioms).
% 3.26/1.55 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.26/1.58 % [INFO] Type checking passed.
% 3.26/1.58 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 14.79/6.03 % External prover 'e' found a proof!
% 14.79/6.03 % [INFO] Killing All external provers ...
% 14.79/6.03 % Time passed: 5525ms (effective reasoning time: 4997ms)
% 14.79/6.03 % 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)>
% 14.79/6.03 % Axioms used in derivation (121): fact_94_atom_Osimps_I2_J, fact_87_map_Osimps_I2_J, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_81_not__Cons__self2, fact_6_assms_I3_J, arity_Int_Oint___Groups_Oone, fact_16_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Rings_Ocomm__ring, fact_3_mod__mod__trivial, fact_93_asubst_Osimps_I1_J, fact_4_add__left__cancel, arity_Int_Oint___Groups_Ominus, fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_72_zmod__simps_I3_J, fact_22_list__add__def, fact_37_iprod__Cons, fact_1_mod__add__self1, fact_23_assms_I2_J, fact_89_scale1, arity_HOL_Obool___Groups_Ominus, arity_Int_Oint___Rings_Oring, fact_11_zmod__simps_I2_J, fact_83_comm__semiring__class_Odistrib, fact_30_list__add__Cons, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Int_Oint___Rings_Ocomm__semiring, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_75_atom_Osimps_I6_J, fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_53_ab__semigroup__mult__class_Omult__ac_I1_J, fact_39_divisor__asubst, fact_67_mod__mult__mult2, fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_12_list__add__assoc, fact_95_list__diff__Cons__Cons, fact_13_add__right__imp__eq, fact_80_not__Cons__self, arity_Int_Oint___Groups_Oplus, fact_74_ext, fact_69_mod__mult__eq, fact_92_asubst_Osimps_I2_J, fact_76_atom_Osimps_I7_J, fact_82_mult__left__idem, fact_43_atom_Osimps_I10_J, arity_List_Olist___Groups_Ominus, fact_90_mult__idem, fact_2_NDvd, fact_28__096_B_Bthesis_O_A_I_B_Bks_H_O_Aks_A_061_A1_A_D_Aks_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_44_atom_Orecs_I1_J, arity_List_Olist___Groups_Oplus, fact_66_zmod__simps_I4_J, fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_64_mult__1__left, fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_18_zmod__simps_I1_J, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Int_Oint___Groups_Omonoid__mult, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_91_times_Oidem, fact_98_square__diff__square__factored, fact_15_add__left__imp__eq, fact_36_atom_Orecs_I3_J, fact_14_add__imp__eq, fact_63_mult__1, fact_41_mod__mult__self1, fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_71_mod__mult__right__eq, fact_9_mod__add__left__eq, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_73_zmod__zmult1__eq, fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_40_atom_Osimps_I1_J, arity_Int_Oint___Rings_Osemiring, fact_70_mod__mult__left__eq, arity_Int_Oint___Groups_Omonoid__add, fact_7_iprod__left__add__distrib, fact_85_IZ__asubst, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_31_one__reorient, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_65_mod__mult__cong, fact_5_add__right__cancel, fact_62_mult__1__right, fact_97_eq__add__iff2, fact_19_atom_Osimps_I3_J, fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_10_mod__add__eq, fact_86_asubst_Osimps_I3_J, arity_Int_Oint___Groups_Oab__semigroup__add, fact_20__096ks_A_061_A1_A_D_Aks_H_096, fact_42_mod__mult__self2, fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_68_mod__mult__mult1, fact_58_crossproduct__eq, fact_29_zipwith0_Osimps_I2_J, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_35_atom_Osimps_I12_J, fact_61_mult_Ocomm__neutral, fact_55_crossproduct__noteq, fact_96_eq__add__iff1, fact_21_divisor_Osimps_I3_J, arity_Int_Oint___Divides_Osemiring__div, fact_88_iprod__assoc, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_38_divisor_Osimps_I1_J, arity_Int_Oint___Groups_Ozero, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_84_combine__common__factor, fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_34_list_Oinject, arity_fun___Groups_Ominus, fact_8_mod__add__right__eq, fact_17_mod__add__cong, fact_0_mod__add__self2, fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 14.79/6.03 % No. of inferences in proof: 246
% 14.79/6.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5525 ms resp. 4997 ms w/o parsing
% 15.22/6.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.22/6.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------