%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM043_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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:57:57 AM UTC 2026
% Result : Theorem 10.24s 3.70s
% Output : Refutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 133
% Syntax : Number of formulae : 268 ( 110 unt; 0 typ; 0 def)
% Number of atoms : 569 ( 304 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2351 ( 16 ~; 0 |; 38 &;2066 @)
% ( 21 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 11 con; 0-4 aty)
% Number of variables : 522 ( 0 ^; 522 !; 0 ?; 522 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_decl,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(uminus_decl,type,
uminus:
!>[TA: $tType] : $o ).
thf(ring_div_decl,type,
ring_div:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[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(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(div_mod_decl,type,
div_mod:
!>[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 > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(nat_is_nat_decl,type,
nat_is_nat: int > $o ).
thf(nDvd_decl,type,
nDvd: int > int > ( int @ list ) > atom ).
thf(atom_size_decl,type,
atom_size: atom > nat ).
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(ks1_decl,type,
ks1: int @ list ).
thf(ks_decl,type,
ks: int @ list ).
thf(l_decl,type,
l: int ).
thf(106,axiom,
! [A: int,B: int] :
( ( B @ nat_is_nat )
=> ( ( A @ nat_is_nat )
=> ( A @ ( B @ ( int @ div_mod ) ) @ nat_is_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Divides_Otransfer__int__nat__function__closures_I2_J) ).
thf(499,plain,
! [A: int,B: int] :
( ( B @ nat_is_nat )
=> ( ( A @ nat_is_nat )
=> ( A @ ( B @ ( int @ div_mod ) ) @ nat_is_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_nat__add__assoc) ).
thf(150,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__right__imp__eq) ).
thf(386,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__0) ).
thf(347,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__is__0) ).
thf(249,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mod__0) ).
thf(555,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(117,axiom,
int @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(523,plain,
int @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(112,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(511,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= A )
<=> ( ( A @ ( TA @ uminus_uminus ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_minus__equation__iff) ).
thf(269,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( TA @ uminus_uminus ) )
= B )
=> ( ( B @ ( TA @ uminus_uminus ) )
= A ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= A )
=> ( ( A @ ( TA @ uminus_uminus ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(129,axiom,
int @ one_one @ nat_is_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
thf(550,plain,
int @ one_one @ nat_is_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(93,axiom,
( a
= ( ks @ ( l @ ( d @ nDvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_NDvd) ).
thf(472,plain,
( a
= ( ks @ ( l @ ( d @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(123,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(538,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__add__left__cancel) ).
thf(153,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__0__iff) ).
thf(174,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(301,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ( ( TA @ zero_zero @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_minus__zero) ).
thf(389,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ( ( TA @ zero_zero @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ uminus ) )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ list @ uminus_uminus ) )
= ( A @ ( TA @ list @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__uminus__Cons) ).
thf(184,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ uminus ) )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ list @ uminus_uminus ) )
= ( A @ ( TA @ list @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,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 ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_list__add__Cons) ).
thf(344,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 ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(61,axiom,
! [TA: $tType] :
( ( ( TA @ uminus )
& ( TA @ zero ) )
=> ( TA @ list @ uminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ouminus) ).
thf(357,plain,
! [TA: $tType] :
( ( ( TA @ uminus )
& ( TA @ zero ) )
=> ( TA @ list @ uminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_mod__add__left__eq) ).
thf(460,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( ( TA @ zero_zero )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_neg__0__equal__iff__equal) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( ( TA @ zero_zero )
= A )
=> ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( ( TA @ zero_zero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_minus__add__distrib) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_one__reorient) ).
thf(316,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)],[50]) ).
thf(9,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(164,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)],[9]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ uminus_uminus ) )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_neg__equal__zero) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ uminus_uminus ) )
= A ) )
& ( ( ( A @ ( TA @ uminus_uminus ) )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(28,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_atom_Osize_I6_J) ).
thf(238,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zmod__simps_I1_J) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__0__right) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(48,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(312,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(113,axiom,
! [A: int] :
( ( A @ ( A @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zmod__self) ).
thf(512,plain,
! [A: int] :
( ( A @ ( A @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(127,axiom,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zmod__zminus__zminus) ).
thf(546,plain,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(201,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(121,axiom,
int @ ring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
thf(534,plain,
int @ ring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( B @ ( TA @ uminus_uminus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__eq__0__iff) ).
thf(302,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A
= ( B @ ( TA @ uminus_uminus ) ) )
=> ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( B @ ( TA @ uminus_uminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(392,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(43,axiom,
bool @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ouminus) ).
thf(297,plain,
bool @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(424,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat__add__left__commute) ).
thf(137,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(90,axiom,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( l @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096_Il_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_J_Amod_Ad_A_061_Il_Amod_Ad_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_J_Amod_Ad_096) ).
thf(467,plain,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( l @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmod__zminus2) ).
thf(484,plain,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(197,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(130,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(551,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_eq__neg__iff__add__eq__0) ).
thf(324,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_uminus__apply) ).
thf(285,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__imp__eq) ).
thf(225,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ uminus )
=> ( TA @ ( TB @ fun ) @ uminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ouminus) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ uminus )
=> ( TA @ ( TB @ fun ) @ uminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(22,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_plus__nat_Oadd__0) ).
thf(212,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(114,axiom,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(515,plain,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(85,axiom,
int @ cl_Groups_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(457,plain,
int @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(30,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(244,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__left__imp__eq) ).
thf(266,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equal__neg__zero) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( A
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( A
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(73,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_61_atom_Osimps_I3_J) ).
thf(398,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)],[73]) ).
thf(133,axiom,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( l @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( int @ div_mod ) ) @ ( d @ ( i @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_calculation) ).
thf(558,plain,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( l @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( int @ div_mod ) ) @ ( d @ ( i @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) @ ( d @ ( l @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_right__minus) ).
thf(298,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_compl__eq__compl__iff) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Oboolean__algebra) ).
thf(148,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__add__commute) ).
thf(161,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(296,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__right__cancel) ).
thf(444,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(75,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(423,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(40,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(291,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( A
= ( B @ ( TA @ uminus_uminus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_equation__minus__iff) ).
thf(204,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A
= ( B @ ( TA @ uminus_uminus ) ) )
=> ( B
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( B
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( A
= ( B @ ( TA @ uminus_uminus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(126,axiom,
int @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(545,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_double__zero__sym) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus ) ) @ ( TA @ list @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus ) ) @ ( C @ ( TA @ list @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list__add__assoc) ).
thf(313,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus ) ) @ ( TA @ list @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus ) ) @ ( C @ ( TA @ list @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(89,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(466,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TB @ ( TA @ fun ),B: TA] :
( ( B @ ( A @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fun__Compl__def) ).
thf(335,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ uminus )
=> ! [A: TB @ ( TA @ fun ),B: TA] :
( ( B @ ( A @ ( TB @ ( TA @ fun ) @ uminus_uminus ) @ ( TB @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_iprod__left__add__distrib) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_neg__equal__iff__equal) ).
thf(350,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(187,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,axiom,
! [A: int,B: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zminus__zmod) ).
thf(451,plain,
! [A: int,B: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(31,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(245,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(111,axiom,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( int @ div_mod ) ) @ ( d @ ( i @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_A_061_Ii_Amod_Ad_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_Amod_Ad_J_Amod_Ad_096) ).
thf(509,plain,
( ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) )
= ( d @ ( d @ ( e @ ( ks1 @ ( int @ iprod ) ) @ ( int @ div_mod ) ) @ ( d @ ( i @ ( int @ div_mod ) ) @ ( int @ plus_plus ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(95,axiom,
int @ uminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ouminus) ).
thf(477,plain,
int @ uminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(103,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(494,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ div_mod ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mod__by__0) ).
thf(535,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ div_mod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__add__right__cancel) ).
thf(140,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(98,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(483,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(116,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 @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_mod__add__cong) ).
thf(520,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 @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(64,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_divisor_Osimps_I3_J) ).
thf(367,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(131,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mod__add__self2) ).
thf(552,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1,conjecture,
( ( d @ ( i @ ( int @ div_mod ) ) )
= ( d @ ( j @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( d @ ( i @ ( int @ div_mod ) ) )
!= ( d @ ( j @ ( int @ div_mod ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(135,plain,
( ( d @ ( i @ ( int @ div_mod ) ) )
!= ( d @ ( j @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ uminus_uminus ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( TA @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_iprod__uminus) ).
thf(241,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ uminus_uminus ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( TA @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
bool @ boolean_algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Oboolean__algebra) ).
thf(167,plain,
bool @ boolean_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(109,axiom,
int @ zero_zero @ nat_is_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
thf(505,plain,
int @ zero_zero @ nat_is_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_atom_Osize_I3_J) ).
thf(438,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(101,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(490,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_mod__add__right__eq) ).
thf(531,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mod__by__1) ).
thf(487,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( B @ nat_is_nat )
=> ( ( A @ nat_is_nat )
=> ( A @ ( B @ ( int @ plus_plus ) ) @ nat_is_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
thf(458,plain,
! [A: int,B: int] :
( ( B @ nat_is_nat )
=> ( ( A @ nat_is_nat )
=> ( A @ ( B @ ( int @ plus_plus ) ) @ nat_is_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(52,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(331,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_double__compl) ).
thf(441,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( B @ ( TA @ uminus_uminus ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_minus__unique) ).
thf(370,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( B @ ( TA @ uminus_uminus ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(108,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_2_mod__mod__trivial) ).
thf(502,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)],[108]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ ring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( B @ ( C @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_mod__minus__cong) ).
thf(463,plain,
! [TA: $tType] :
( ( TA @ ring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( B @ ( C @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(55,axiom,
nat @ cl_Groups_Oplus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oplus) ).
thf(338,plain,
nat @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(92,axiom,
( ks
= ( ks1 @ ( int @ one_one @ ( int @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096ks_A_061_A1_A_D_Aks_H_096) ).
thf(470,plain,
( ks
= ( ks1 @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(62,axiom,
nat @ semiring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Divides_Osemiring__div) ).
thf(359,plain,
nat @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(125,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(544,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_double__eq__0__iff) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(124,axiom,
~ ! [A: int @ list] :
( ks
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86__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(539,plain,
~ ! [A: int @ list] :
( ks
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(118,axiom,
! [A: int] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_odd__nonzero) ).
thf(524,plain,
! [A: int] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(104,axiom,
int @ ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(495,plain,
int @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_neg__equal__0__iff__equal) ).
thf(218,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mod__add__self1) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add_Ocomm__neutral) ).
thf(171,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_left__minus) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(96,axiom,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_assms_I2_J) ).
thf(478,plain,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ab__left__minus) ).
thf(383,plain,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(128,axiom,
int @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(549,plain,
int @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__0__left) ).
thf(168,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__left__cancel) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_minus__add__cancel) ).
thf(373,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(341,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) )
=> ( ( A @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_zmod__zminus2__not__zero) ).
thf(506,plain,
! [A: int,B: int] :
( ( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) )
=> ( ( A @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(79,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(437,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(94,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zmod__zero) ).
thf(474,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ div_mod ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_minus__minus) ).
thf(395,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( TA @ uminus_uminus ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__minus__cancel) ).
thf(332,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(427,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zmod__simps_I2_J) ).
thf(528,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zero__reorient) ).
thf(277,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(107,axiom,
int @ semiring_div,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(501,plain,
int @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(91,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(469,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(309,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( B @ ( TA @ uminus_uminus ) @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_minus__add) ).
thf(215,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( B @ ( TA @ uminus_uminus ) @ ( A @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_mod__self) ).
thf(560,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ div_mod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(102,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) )
=> ( ( A @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_zmod__zminus1__not__zero) ).
thf(491,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ uminus_uminus ) @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) )
=> ( ( A @ ( B @ ( int @ div_mod ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mod__add__eq) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ ring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__minus__eq) ).
thf(454,plain,
! [TA: $tType] :
( ( TA @ ring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ uminus_uminus ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(577,plain,
$false,
inference(e,[status(thm)],[499,150,386,347,249,555,523,511,269,550,472,538,153,174,288,301,389,184,344,357,460,416,228,316,164,376,238,480,293,312,512,546,201,534,302,392,297,424,137,467,484,197,551,324,285,225,339,212,515,457,244,266,360,398,558,298,430,148,161,296,444,423,291,204,545,259,313,466,335,181,350,187,451,245,509,477,494,535,140,483,520,198,367,552,135,241,167,505,438,490,531,487,458,331,441,370,502,463,338,470,359,544,231,539,524,495,218,517,171,246,478,383,549,168,190,373,341,506,437,474,395,332,427,528,277,501,469,309,215,560,491,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM043_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 23:24:36 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.26 % [INFO] Parsing done (284ms).
% 1.48/1.27 % [INFO] Running in sequential loop mode.
% 2.32/1.66 % [INFO] eprover registered as external prover.
% 2.32/1.67 % [INFO] Scanning for conjecture ...
% 2.71/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 134 axioms. Running axiom selection ...
% 2.90/1.93 % [INFO] Axiom selection finished. Selected 132 axioms (removed 2 axioms).
% 3.42/2.07 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.42/2.08 % [INFO] Type checking passed.
% 3.42/2.08 % [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 ...
% 10.24/3.70 % External prover 'e' found a proof!
% 10.24/3.70 % [INFO] Killing All external provers ...
% 10.24/3.70 % Time passed: 3159ms (effective reasoning time: 2422ms)
% 10.24/3.70 % 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)>
% 10.24/3.70 % Axioms used in derivation (132): fact_8_Divides_Otransfer__int__nat__function__closures_I2_J, arity_HOL_Obool___Groups_Ouminus, arity_Int_Oint___Groups_Ouminus, fact_64_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J, fact_89_list__add__Cons, fact_25_zmod__zminus2, fact_12_mod__add__self2, fact_83__096ks_A_061_A1_A_D_Aks_H_096, fact_4__096_Il_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_J_Amod_Ad_A_061_Il_Amod_Ad_A_L_A_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_J_Amod_Ad_096, arity_Int_Oint___Groups_Oone, fact_15_zmod__zminus1__not__zero, fact_23_mod__add__right__eq, fact_41_add__right__imp__eq, fact_30_minus__add__distrib, fact_9_mod__0, fact_20_zmod__simps_I2_J, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_65_list__add__assoc, fact_61_atom_Osimps_I3_J, fact_32_neg__0__equal__iff__equal, fact_5_calculation, fact_49_add__0__right, arity_Int_Oint___Rings_Oring, arity_HOL_Obool___Lattices_Oboolean__algebra, fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, arity_Int_Oint___Groups_Oab__group__add, fact_7_zmod__self, fact_97_plus__nat_Oadd__0, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Nat_Onat___Groups_Oplus, fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, arity_Nat_Onat___Divides_Osemiring__div, fact_54_minus__add, fact_92_one__reorient, fact_22_mod__add__left__eq, fact_86__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_2_mod__mod__trivial, fact_43_add__left__imp__eq, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_93_nat__add__commute, fact_40_zero__reorient, fact_74_ext, fact_90_list__uminus__Cons, fact_95_nat__add__assoc, arity_Int_Oint___Groups_Oplus, fact_13_mod__add__self1, arity_List_Olist___Groups_Ouminus, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_19_zmod__simps_I1_J, fact_17_mod__minus__eq, fact_14_zmod__zminus2__not__zero, fact_85_nat__add__right__cancel, fact_38_neg__equal__iff__equal, fact_50_add__0, fact_10_mod__self, fact_42_add__imp__eq, arity_Int_Oint___Divides_Oring__div, fact_80_add__0__iff, fact_46_equation__minus__iff, fact_53_add__minus__cancel, arity_List_Olist___Groups_Oplus, fact_48_add_Ocomm__neutral, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_fun___Groups_Ouminus, fact_31_minus__zero, fact_44_ab__semigroup__add__class_Oadd__ac_I1_J, fact_82_add__is__0, fact_16_mod__minus__cong, fact_84_nat__add__left__cancel, fact_57_add__eq__0__iff, fact_36_add__right__cancel, fact_70_atom_Osize_I3_J, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Int_Oint___Groups_Omonoid__add, arity_Nat_Onat___Groups_Ozero, fact_52_minus__add__cancel, fact_69_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J, fact_96_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J, fact_37_add__left__cancel, fact_67_double__compl, fact_1_assms_I3_J, fact_18_mod__add__cong, fact_29_iprod__uminus, fact_68_uminus__apply, arity_fun___Lattices_Oboolean__algebra, arity_Int_Oint___Groups_Ogroup__add, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_58_ab__left__minus, fact_11_zmod__zminus__zminus, fact_21_mod__add__eq, fact_47_minus__minus, fact_87_assms_I2_J, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_62_compl__eq__compl__iff, fact_60_double__eq__0__iff, fact_6_zmod__zero, fact_55_iprod__left__add__distrib, fact_39_double__zero__sym, fact_0_NDvd, fact_59_eq__neg__iff__add__eq__0, fact_28_left__minus, fact_88_mod__by__1, arity_Nat_Onat___Groups_Oone, arity_Int_Oint___Groups_Oab__semigroup__add, fact_3__096_Ii_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_J_Amod_Ad_A_061_Ii_Amod_Ad_A_L_A_092_060langle_062ks_H_Me_092_060rangle_062_Amod_Ad_J_Amod_Ad_096, fact_33_equal__neg__zero, fact_71_atom_Osize_I6_J, fact_35_neg__equal__zero, arity_Nat_Onat___Groups_Omonoid__add, arity_Int_Oint___Divides_Osemiring__div, fact_27_right__minus, fact_51_add__0__left, fact_91_odd__nonzero, fact_34_neg__equal__0__iff__equal, fact_24_zminus__zmod, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_56_minus__unique, fact_45_minus__equation__iff, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_94_nat__add__left__commute, fact_26_mod__by__0, fact_66_fun__Compl__def, fact_63_divisor_Osimps_I3_J
% 10.24/3.70 % No. of inferences in proof: 268
% 10.24/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3159 ms resp. 2422 ms w/o parsing
% 10.65/3.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.65/3.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------