TSTP Solution File: COM035_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM035_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:13:57 EDT 2023
% Result : Theorem 7.32s 2.81s
% Output : Refutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 177
% Syntax : Number of formulae : 312 ( 110 unt; 44 typ; 0 def)
% Number of atoms : 569 ( 304 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2361 ( 16 ~; 0 |; 38 &;2076 @)
% ( 21 <=>; 210 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 11 con; 0-4 aty)
% Number of variables : 550 ( 0 ^; 522 !; 0 ?; 550 :)
% ( 28 !>; 0 ?*; 0 @-; 0 @+)
% 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_type,type,
one:
!>[TA: $tType] : $o ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_type,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : $o ).
thf(ring_div_type,type,
ring_div:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(semiring_div_type,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(div_mod_type,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iprod_type,type,
iprod:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > TA ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(nat_is_nat_type,type,
nat_is_nat: int > $o ).
thf(dvd_type,type,
dvd: int > int > ( list @ int ) > atom ).
thf(atom_size_type,type,
atom_size: atom > nat ).
thf(divisor_type,type,
divisor: atom > int ).
thf(hd_coeff_type,type,
hd_coeff: atom > int ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(a_type,type,
a: atom ).
thf(d_type,type,
d: int ).
thf(e_type,type,
e: list @ int ).
thf(i_type,type,
i: int ).
thf(j_type,type,
j: int ).
thf(ks1_type,type,
ks1: list @ int ).
thf(ks_type,type,
ks: list @ int ).
thf(l_type,type,
l: int ).
thf(98,axiom,
! [A: int,B: int] :
( ( div_mod @ int @ B @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ int @ ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmod__zminus2) ).
thf(457,plain,
! [A: int,B: int] :
( ( div_mod @ int @ B @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ int @ ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( ( div_mod @ int @ B @ ( uminus_uminus @ int @ A ) )
!= ( zero_zero @ int ) )
=> ( ( div_mod @ int @ B @ A )
!= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_zmod__zminus2__not__zero) ).
thf(479,plain,
! [A: int,B: int] :
( ( ( div_mod @ int @ B @ ( uminus_uminus @ int @ A ) )
!= ( zero_zero @ int ) )
=> ( ( div_mod @ int @ B @ A )
!= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(125,axiom,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zmod__zero) ).
thf(518,plain,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(103,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(468,plain,
ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(40,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(276,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(50,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(308,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(122,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(511,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_atom_Osize_I2_J) ).
thf(384,plain,
! [A: list @ int,B: int,C: int] :
( ( atom_size @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(105,axiom,
! [A: int,B: int] :
( ( nat_is_nat @ B )
=> ( ( nat_is_nat @ A )
=> ( nat_is_nat @ ( div_mod @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Divides_Otransfer__int__nat__function__closures_I2_J) ).
thf(472,plain,
! [A: int,B: int] :
( ( nat_is_nat @ B )
=> ( ( nat_is_nat @ A )
=> ( nat_is_nat @ ( div_mod @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(79,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(417,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(45,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(288,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(87,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_mod__add__left__eq) ).
thf(436,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(16,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(184,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
<=> ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_neg__0__equal__iff__equal) ).
thf(372,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
=> ( ( zero_zero @ TA )
= A ) )
& ( ( ( zero_zero @ TA )
= A )
=> ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_mod__add__right__eq) ).
thf(504,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ab__left__minus) ).
thf(357,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(99,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mod__by__1) ).
thf(460,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__add__left__cancel) ).
thf(152,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(228,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(93,axiom,
( ks
= ( cons @ int @ ( one_one @ int ) @ ks1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096ks_A_061_A1_A_D_Aks_H_096) ).
thf(448,plain,
( ks
= ( cons @ int @ ( one_one @ int ) @ ks1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ouminus) ).
thf(316,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(107,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_mod__mod__trivial) ).
thf(475,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(56,axiom,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( dvd @ C @ B @ A ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_divisor_Osimps_I2_J) ).
thf(321,plain,
! [A: list @ int,B: int,C: int] :
( ( divisor @ ( dvd @ C @ B @ A ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(112,axiom,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zmod__self) ).
thf(485,plain,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(64,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( plus_plus @ TA @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_minus__add__cancel) ).
thf(348,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( plus_plus @ TA @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Oboolean__algebra) ).
thf(147,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(96,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) @ A ) @ B )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zmod__simps_I1_J) ).
thf(453,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) @ A ) @ B )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_double__eq__0__iff) ).
thf(411,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ! [A: TA,B: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( uminus_uminus @ ( fun @ TA @ TB ) @ B ) @ A )
= ( uminus_uminus @ TB @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_uminus__apply) ).
thf(265,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ! [A: TA,B: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( uminus_uminus @ ( fun @ TA @ TB ) @ B ) @ A )
= ( uminus_uminus @ TB @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(120,axiom,
ring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
thf(507,plain,
ring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(130,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(527,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ! [A: fun @ TA @ TB,B: TA] :
( ( aa @ TA @ TB @ ( uminus_uminus @ ( fun @ TA @ TB ) @ A ) @ B )
= ( uminus_uminus @ TB @ ( aa @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fun__Compl__def) ).
thf(312,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ! [A: fun @ TA @ TB,B: TA] :
( ( aa @ TA @ TB @ ( uminus_uminus @ ( fun @ TA @ TB ) @ A ) @ B )
= ( uminus_uminus @ TB @ ( aa @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(47,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( plus_plus @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ C @ B ) @ A )
= ( plus_plus @ ( list @ TA ) @ C @ ( plus_plus @ ( list @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list__add__assoc) ).
thf(292,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( plus_plus @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ C @ B ) @ A )
= ( plus_plus @ ( list @ TA ) @ C @ ( plus_plus @ ( list @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__is__0) ).
thf(233,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__left__imp__eq) ).
thf(248,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(69,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(366,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(133,axiom,
( ( div_mod @ int @ ( plus_plus @ int @ l @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ l @ d ) @ ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ i @ d ) @ ( div_mod @ int @ ( iprod @ int @ ks1 @ e ) @ d ) ) @ d ) ) @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_calculation) ).
thf(534,plain,
( ( div_mod @ int @ ( plus_plus @ int @ l @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ l @ d ) @ ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ i @ d ) @ ( div_mod @ int @ ( iprod @ int @ ks1 @ e ) @ d ) ) @ d ) ) @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(123,axiom,
~ ! [A: list @ int] :
( ks
!= ( cons @ int @ ( one_one @ int ) @ A ) ),
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(512,plain,
~ ! [A: list @ int] :
( ks
!= ( cons @ int @ ( one_one @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(88,axiom,
( a
= ( dvd @ d @ l @ ks ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Dvd) ).
thf(439,plain,
( a
= ( dvd @ d @ l @ ks ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(49,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( uminus_uminus @ TA @ A ) )
<=> ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_eq__neg__iff__add__eq__0) ).
thf(302,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( uminus_uminus @ TA @ A ) )
=> ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) ) )
& ( ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( B
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(82,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_double__compl) ).
thf(424,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_atom_Osize_I5_J) ).
thf(407,plain,
! [A: list @ int,B: int,C: int] :
( ( size_size @ atom @ ( dvd @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat__add__left__commute) ).
thf(137,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
boolean_algebra @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Oboolean__algebra) ).
thf(165,plain,
boolean_algebra @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(102,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(467,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(197,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(127,axiom,
! [A: int,B: int] :
( ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ int @ ( div_mod @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zmod__zminus__zminus) ).
thf(522,plain,
! [A: int,B: int] :
( ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ ( uminus_uminus @ int @ A ) )
= ( uminus_uminus @ int @ ( div_mod @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(115,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( plus_plus @ TA @ E @ B ) @ D )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_mod__add__cong) ).
thf(493,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( plus_plus @ TA @ E @ B ) @ D )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(97,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(456,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( plus_plus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ ( list @ TA ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_list__add__Cons) ).
thf(324,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( plus_plus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ ( list @ TA ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(229,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(111,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(484,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(12,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add_Ocomm__neutral) ).
thf(169,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(80,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(420,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(113,axiom,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(488,plain,
( ( div_mod @ int @ i @ ( divisor @ a ) )
= ( div_mod @ int @ j @ ( divisor @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(27,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( iprod @ TA @ ( uminus_uminus @ ( list @ TA ) @ B ) @ A )
= ( uminus_uminus @ TA @ ( iprod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_iprod__uminus) ).
thf(225,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( iprod @ TA @ ( uminus_uminus @ ( list @ TA ) @ B ) @ A )
= ( uminus_uminus @ TA @ ( iprod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equal__neg__zero) ).
thf(339,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( A
= ( uminus_uminus @ TA @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( A
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(193,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(129,axiom,
nat_is_nat @ ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
thf(526,plain,
nat_is_nat @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(67,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__right__imp__eq) ).
thf(360,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(121,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mod__by__0) ).
thf(508,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( uminus_uminus @ TA @ B ) @ A )
= ( div_mod @ TA @ ( uminus_uminus @ TA @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_mod__minus__eq) ).
thf(430,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( uminus_uminus @ TA @ B ) @ A )
= ( div_mod @ TA @ ( uminus_uminus @ TA @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(11,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__0__left) ).
thf(166,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(90,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(444,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_nat__add__assoc) ).
thf(149,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(81,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(423,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(46,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(291,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(43,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(281,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(91,axiom,
( ( div_mod @ int @ ( plus_plus @ int @ l @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ l @ d ) @ ( div_mod @ int @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) @ d ) ) @ d ) ),
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(445,plain,
( ( div_mod @ int @ ( plus_plus @ int @ l @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ l @ d ) @ ( div_mod @ int @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) @ d ) ) @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( uminus_uminus @ ( list @ TA ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ ( list @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__uminus__Cons) ).
thf(181,plain,
! [TA: $tType] :
( ( ( uminus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA] :
( ( uminus_uminus @ ( list @ TA ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ ( list @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__add__commute) ).
thf(159,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__left__cancel) ).
thf(187,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( plus_plus @ TA @ B @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__0__iff) ).
thf(172,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( plus_plus @ TA @ B @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__imp__eq) ).
thf(219,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_left__minus) ).
thf(230,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(95,axiom,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_assms_I2_J) ).
thf(451,plain,
( ( hd_coeff @ a )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(55,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(318,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( nat_is_nat @ B )
=> ( ( nat_is_nat @ A )
=> ( nat_is_nat @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
thf(434,plain,
! [A: int,B: int] :
( ( nat_is_nat @ B )
=> ( ( nat_is_nat @ A )
=> ( nat_is_nat @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(271,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_atom_Osimps_I2_J) ).
thf(387,plain,
! [A: list @ int,B: int,C: int,D: list @ int,E: int,F: int] :
( ( ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( dvd @ F @ E @ D )
= ( dvd @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(63,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_minus__unique) ).
thf(345,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__add__right__cancel) ).
thf(140,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_neg__equal__0__iff__equal) ).
thf(213,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ B )
= A )
<=> ( ( uminus_uminus @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_minus__equation__iff) ).
thf(251,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( uminus_uminus @ TA @ B )
= A )
=> ( ( uminus_uminus @ TA @ A )
= B ) )
& ( ( ( uminus_uminus @ TA @ A )
= B )
=> ( ( uminus_uminus @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(59,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_neg__equal__iff__equal) ).
thf(330,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(126,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(521,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(42,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_right__minus) ).
thf(278,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1,conjecture,
( ( div_mod @ int @ i @ d )
= ( div_mod @ int @ j @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( div_mod @ int @ i @ d )
!= ( div_mod @ int @ j @ d ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(135,plain,
( ( div_mod @ int @ i @ d )
!= ( div_mod @ int @ j @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(114,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mod__add__self1) ).
thf(490,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(19,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(194,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(162,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(132,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_mod__0) ).
thf(531,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(128,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(525,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(48,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_one__reorient) ).
thf(295,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(44,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__eq__0__iff) ).
thf(282,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( uminus_uminus @ TA @ B ) ) )
& ( ( A
= ( uminus_uminus @ TA @ B ) )
=> ( ( plus_plus @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(58,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__0) ).
thf(327,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( div_mod @ TA @ C @ B )
= ( div_mod @ TA @ A @ B ) )
=> ( ( div_mod @ TA @ ( uminus_uminus @ TA @ C ) @ B )
= ( div_mod @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_mod__minus__cong) ).
thf(441,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( div_mod @ TA @ C @ B )
= ( div_mod @ TA @ A @ B ) )
=> ( ( div_mod @ TA @ ( uminus_uminus @ TA @ C ) @ B )
= ( div_mod @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(100,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(463,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(61,axiom,
semiring_div @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Divides_Osemiring__div) ).
thf(338,plain,
semiring_div @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(60,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( uminus @ TA ) )
=> ( uminus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ouminus) ).
thf(336,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( uminus @ TA ) )
=> ( uminus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(117,axiom,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_odd__nonzero) ).
thf(497,plain,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(94,axiom,
uminus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ouminus) ).
thf(450,plain,
uminus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(68,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_minus__zero) ).
thf(363,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(110,axiom,
( ( div_mod @ int @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ i @ d ) @ ( div_mod @ int @ ( iprod @ int @ ks1 @ e ) @ d ) ) @ d ) ),
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(482,plain,
( ( div_mod @ int @ ( plus_plus @ int @ i @ ( iprod @ int @ ks1 @ e ) ) @ d )
= ( div_mod @ int @ ( plus_plus @ int @ ( div_mod @ int @ i @ d ) @ ( div_mod @ int @ ( iprod @ int @ ks1 @ e ) @ d ) ) @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(124,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(517,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(35,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zero__reorient) ).
thf(258,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_neg__equal__zero) ).
thf(351,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( uminus_uminus @ TA @ A )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(75,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__right__cancel) ).
thf(401,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(72,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_compl__eq__compl__iff) ).
thf(378,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(85,axiom,
cl_Groups_Oplus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(433,plain,
cl_Groups_Oplus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(22,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_plus__nat_Oadd__0) ).
thf(207,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(108,axiom,
nat_is_nat @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
thf(478,plain,
nat_is_nat @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(134,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_mod__self) ).
thf(536,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(92,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(447,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(53,axiom,
cl_Groups_Oplus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oplus) ).
thf(315,plain,
cl_Groups_Oplus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(410,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(39,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__0__right) ).
thf(273,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_minus__add) ).
thf(210,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_double__zero__sym) ).
thf(242,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(268,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(106,axiom,
semiring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(474,plain,
semiring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(101,axiom,
! [A: int,B: int] :
( ( ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A )
!= ( zero_zero @ int ) )
=> ( ( div_mod @ int @ B @ A )
!= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_zmod__zminus1__not__zero) ).
thf(464,plain,
! [A: int,B: int] :
( ( ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A )
!= ( zero_zero @ int ) )
=> ( ( div_mod @ int @ B @ A )
!= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(83,axiom,
! [A: int,B: int] :
( ( div_mod @ int @ ( uminus_uminus @ int @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zminus__zmod) ).
thf(427,plain,
! [A: int,B: int] :
( ( div_mod @ int @ ( uminus_uminus @ int @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( uminus_uminus @ int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(131,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mod__add__self2) ).
thf(528,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(21,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( uminus_uminus @ TA @ A ) )
<=> ( A
= ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_equation__minus__iff) ).
thf(200,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( uminus_uminus @ TA @ A ) )
=> ( A
= ( uminus_uminus @ TA @ B ) ) )
& ( ( A
= ( uminus_uminus @ TA @ B ) )
=> ( B
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( plus_plus @ ( list @ TA ) @ C @ B ) @ A )
= ( plus_plus @ TA @ ( iprod @ TA @ C @ A ) @ ( iprod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_iprod__left__add__distrib) ).
thf(178,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( iprod @ TA @ ( plus_plus @ ( list @ TA ) @ C @ B ) @ A )
= ( plus_plus @ TA @ ( iprod @ TA @ C @ A ) @ ( iprod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
uminus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ouminus) ).
thf(277,plain,
uminus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(118,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zmod__simps_I2_J) ).
thf(501,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(70,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_minus__minus) ).
thf(369,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(104,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_mod__add__eq) ).
thf(469,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(51,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__minus__cancel) ).
thf(309,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_minus__add__distrib) ).
thf(222,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( uminus_uminus @ TA @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(496,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(539,plain,
$false,
inference(e,[status(thm)],[457,479,518,468,276,308,511,384,472,417,288,436,184,372,504,357,460,152,228,448,316,475,321,485,348,147,453,411,265,507,527,312,292,233,248,366,534,512,439,302,424,407,137,165,467,197,522,493,456,324,229,484,169,420,488,225,339,193,526,360,508,430,166,444,149,423,291,281,445,181,159,187,172,219,230,451,318,434,271,387,345,140,213,251,330,521,278,135,490,194,162,531,525,295,282,327,441,463,338,336,497,450,363,482,517,258,351,401,378,433,207,478,536,447,315,410,273,210,242,268,474,464,427,528,200,178,277,501,369,469,309,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COM035_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 03:14:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.04 % [INFO] Parsing done (191ms).
% 1.49/1.05 % [INFO] Running in sequential loop mode.
% 1.96/1.27 % [INFO] eprover registered as external prover.
% 1.96/1.27 % [INFO] cvc4 registered as external prover.
% 1.96/1.28 % [INFO] Scanning for conjecture ...
% 2.25/1.37 % [INFO] Found a conjecture and 134 axioms. Running axiom selection ...
% 2.40/1.44 % [INFO] Axiom selection finished. Selected 132 axioms (removed 2 axioms).
% 2.90/1.57 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.90/1.58 % [INFO] Type checking passed.
% 2.90/1.59 % [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 ...
% 7.32/2.80 % External prover 'e' found a proof!
% 7.32/2.80 % [INFO] Killing All external provers ...
% 7.32/2.81 % Time passed: 2295ms (effective reasoning time: 1753ms)
% 7.32/2.81 % 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)>
% 7.32/2.81 % 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_71_atom_Osize_I5_J, 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_0_Dvd, 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_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, fact_70_atom_Osize_I2_J, arity_Int_Oint___Groups_Oab__group__add, fact_63_divisor_Osimps_I2_J, 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, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_61_atom_Osimps_I2_J, 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_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_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_66_fun__Compl__def, fact_94_nat__add__left__commute, fact_26_mod__by__0
% 7.32/2.81 % No. of inferences in proof: 268
% 7.32/2.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2295 ms resp. 1753 ms w/o parsing
% 7.54/2.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.54/2.88 % [INFO] Killing All external provers ...
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