%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM033_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:57:55 AM UTC 2026
% Result : Theorem 17.10s 6.49s
% Output : Refutation 18.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 122
% Syntax : Number of formulae : 246 ( 86 unt; 0 typ; 0 def)
% Number of atoms : 913 ( 283 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 6117 ( 23 ~; 3 |; 45 &;5846 @)
% ( 12 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 11 con; 0-5 aty)
% Number of variables : 770 ( 0 ^; 770 !; 0 ?; 770 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_decl,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_decl,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(comm_ring_decl,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(semiring_div_decl,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_decl,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(div_mod_decl,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > ( TA @ ( TA @ fun ) ) ) ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA ) ).
thf(zipwith0_decl,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ list @ ( TB @ list @ fun ) @ ( TC @ list @ fun ) ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(i_Z_decl,type,
i_Z: atom > ( int @ list ) > $o ).
thf(asubst_decl,type,
asubst: int > ( int @ list ) > atom > atom ).
thf(dvd_decl,type,
dvd: int > int > ( int @ list ) > atom ).
thf(c_PresArith_Oatom_OLe_decl,type,
c_PresArith_Oatom_OLe: int > ( int @ list ) > atom ).
thf(nDvd_decl,type,
nDvd: int > int > ( int @ list ) > atom ).
thf(atom_case_decl,type,
atom_case:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(atom_rec_decl,type,
atom_rec:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(hd_coeff_decl,type,
hd_coeff: atom > int ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(a_decl,type,
a: atom ).
thf(d_decl,type,
d: int ).
thf(e_decl,type,
e: int @ list ).
thf(i_decl,type,
i: int ).
thf(j_decl,type,
j: int ).
thf(ks_decl,type,
ks: int @ list ).
thf(ks1_decl,type,
ks1: int @ list ).
thf(l_decl,type,
l: int ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_mod__mult__mult1) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_mult__left__idem) ).
thf(347,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( C @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mod__mult__self1) ).
thf(333,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( C @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_list__add__def) ).
thf(449,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(26,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(247,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(385,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(72,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(384,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(404,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(84,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zmod__zmult1__eq) ).
thf(417,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(504,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_mod__mult__mult2) ).
thf(344,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__1__right) ).
thf(460,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(289,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_atom_Orecs_I1_J) ).
thf(261,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zipwith0_Osimps_I2_J) ).
thf(443,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(353,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_map_Osimps_I2_J) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA @ list] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_scale1) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA @ list] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_mod__add__eq) ).
thf(280,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_mod__add__self2) ).
thf(507,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_iprod__Cons) ).
thf(292,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) @ ( D @ ( E @ asubst ) ) )
= ( A @ ( D @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ minus_minus ) ) @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_asubst_Osimps_I1_J) ).
thf(248,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) @ ( D @ ( E @ asubst ) ) )
= ( A @ ( D @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ minus_minus ) ) @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(122,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(529,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_mod__add__right__eq) ).
thf(381,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__left__cancel) ).
thf(233,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_mod__mod__trivial) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(18,axiom,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ dvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_atom_Osimps_I5_J) ).
thf(220,plain,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ dvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,axiom,
int @ semiring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(366,plain,
int @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(302,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_mult_Ocomm__neutral) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comm__semiring__class_Odistrib) ).
thf(467,plain,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(21,axiom,
int @ cl_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(229,plain,
int @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_mult__1) ).
thf(252,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_square__diff__square__factored) ).
thf(435,plain,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__add__cong) ).
thf(522,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_list__add__Cons) ).
thf(224,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zmod__simps_I2_J) ).
thf(519,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list__diff__Cons__Cons) ).
thf(188,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_iprod__assoc) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zmod__simps_I1_J) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_divisor__asubst) ).
thf(169,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_mod__mult__right__eq) ).
thf(420,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_mod__add__self1) ).
thf(471,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1,conjecture,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
!= ( d @ ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(124,plain,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
!= ( d @ ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(109,axiom,
( a
= ( ks1 @ ( l @ ( d @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Dvd) ).
thf(489,plain,
( a
= ( ks1 @ ( l @ ( d @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_one__reorient) ).
thf(212,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_atom_Osimps_I3_J) ).
thf(129,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_iprod__left__add__distrib) ).
thf(371,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(78,axiom,
int @ comm_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
thf(398,plain,
int @ comm_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_combine__common__factor) ).
thf(530,plain,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(45,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(298,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(513,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(166,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(264,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(423,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_atom_Osimps_I2_J) ).
thf(191,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(41,axiom,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ nDvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I3_J) ).
thf(286,plain,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ nDvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zmod__simps_I4_J) ).
thf(391,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__idem) ).
thf(498,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(100,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(466,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(350,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(12,axiom,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_atom_Osimps_I1_J) ).
thf(172,plain,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) )
& ( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_times_Oidem) ).
thf(274,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list__add__assoc) ).
thf(230,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
int @ ab_semigroup_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(362,plain,
int @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mod__add__left__eq) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(477,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(67,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(367,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_crossproduct__eq) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mod__mult__cong) ).
thf(483,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(24,axiom,
int @ cl_Groups_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(240,plain,
int @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(251,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(79,axiom,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_assms_I2_J) ).
thf(399,plain,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(97,axiom,
~ ! [A: int @ list] :
( ks1
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
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(455,plain,
~ ! [A: int @ list] :
( ks1
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(46,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_atom_Osimps_I11_J) ).
thf(299,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(438,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(25,axiom,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) )
<=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_IZ__asubst) ).
thf(241,plain,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) )
=> ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) ) )
& ( ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) )
=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(76,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(394,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
thf(306,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(87,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_divisor_Osimps_I1_J) ).
thf(426,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__right__cancel) ).
thf(374,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(255,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_not__Cons__self) ).
thf(209,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(117,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_atom_Orecs_I2_J) ).
thf(516,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(525,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(44,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_atom_Osimps_I10_J) ).
thf(295,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(6,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_atom_Osimps_I4_J) ).
thf(150,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(92,axiom,
( ks1
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__096ks_A_061_A1_A_D_Aks_H_096) ).
thf(441,plain,
( ks1
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(99,axiom,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ dvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_asubst_Osimps_I2_J) ).
thf(463,plain,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ dvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(102,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(470,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(359,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(7,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list_Oinject) ).
thf(154,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
thf(446,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_mod__mult__left__eq) ).
thf(363,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_mod__mult__eq) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(319,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(186,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(401,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
thf(432,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_eq__add__iff2) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,axiom,
bool @ cl_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(168,plain,
bool @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(305,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_divisor_Osimps_I2_J) ).
thf(126,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zmod__simps_I3_J) ).
thf(341,plain,
! [A: int,B: int,C: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_mult__1__left) ).
thf(474,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(395,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(121,axiom,
int @ comm_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(528,plain,
int @ comm_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__Cons__self2) ).
thf(163,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(277,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( C @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mod__mult__self2) ).
thf(501,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( C @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(20,axiom,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms_I3_J) ).
thf(227,plain,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
int @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(322,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_crossproduct__noteq) ).
thf(309,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_eq__add__iff1) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(536,plain,
$false,
inference(e,[status(thm)],[510,347,333,449,247,385,384,404,417,504,344,460,289,261,443,353,480,147,280,265,507,292,248,529,381,233,452,220,366,302,407,429,467,229,252,435,522,224,519,188,388,356,169,420,471,124,339,489,212,129,371,398,530,298,513,166,264,423,191,286,391,498,466,350,172,274,230,362,271,477,367,323,483,240,251,399,455,299,438,241,394,306,426,374,255,209,516,525,295,150,441,463,470,359,336,154,446,363,368,319,258,186,401,432,410,168,305,126,341,268,474,283,395,528,163,277,501,227,322,486,309,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM033_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 23:23:40 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.70/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/0.94 % [INFO] Parsing done (221ms).
% 1.36/0.96 % [INFO] Running in sequential loop mode.
% 2.35/1.35 % [INFO] eprover registered as external prover.
% 2.35/1.36 % [INFO] Scanning for conjecture ...
% 2.76/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 3.01/1.66 % [INFO] Axiom selection finished. Selected 121 axioms (removed 2 axioms).
% 4.18/1.92 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.18/1.96 % [INFO] Type checking passed.
% 4.18/1.96 % [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 ...
% 17.10/6.49 % External prover 'e' found a proof!
% 17.10/6.49 % [INFO] Killing All external provers ...
% 17.10/6.49 % Time passed: 5992ms (effective reasoning time: 5526ms)
% 17.10/6.49 % 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)>
% 17.10/6.49 % Axioms used in derivation (121): fact_2_Dvd, fact_87_map_Osimps_I2_J, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_81_not__Cons__self2, fact_97_eq__add__iff2, 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, fact_75_atom_Osimps_I4_J, 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_36_atom_Orecs_I2_J, 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_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_92_asubst_Osimps_I3_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_35_atom_Osimps_I11_J, fact_82_mult__left__idem, fact_43_atom_Osimps_I10_J, arity_List_Olist___Groups_Ominus, fact_90_mult__idem, 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_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_86_asubst_Osimps_I2_J, 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_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_10_mod__add__eq, 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_21_divisor_Osimps_I2_J, fact_68_mod__mult__mult1, fact_94_atom_Osimps_I3_J, 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_61_mult_Ocomm__neutral, fact_55_crossproduct__noteq, fact_96_eq__add__iff1, 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_19_atom_Osimps_I2_J, 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_76_atom_Osimps_I5_J, fact_0_mod__add__self2, fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 17.10/6.49 % No. of inferences in proof: 246
% 17.10/6.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5992 ms resp. 5526 ms w/o parsing
% 18.17/6.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.17/6.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------