TSTP Solution File: LCL837-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 11:32:15 EDT 2023
% Result : Unsatisfiable 11.58s 3.45s
% Output : Refutation 12.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 752
% Syntax : Number of formulae : 1408 ( 329 unt; 97 typ; 0 def)
% Number of atoms : 2963 (1008 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 18326 (1530 ~;1652 |; 0 &;15144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 97 usr; 17 con; 0-6 aty)
% Number of variables : 3388 ( 0 ^;3388 !; 0 ?;3388 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
thf(v_r_____type,type,
v_r____: $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i ).
thf(v_u_____type,type,
v_u____: $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(v_i_____type,type,
v_i____: $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(v_as_____type,type,
v_as____: $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(v_T_____type,type,
v_T____: $i ).
thf(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1: $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Lambda_Osubstn_type,type,
c_Lambda_Osubstn: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(v_sko__Nat__Xnat__Xinducts__1_type,type,
v_sko__Nat__Xnat__Xinducts__1: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(v_sko__List__Xlexn__Xinduct__1_type,type,
v_sko__List__Xlexn__Xinduct__1: $i > $i ).
thf(v_sko__Nat__Xnat__Xinduct__1_type,type,
v_sko__Nat__Xnat__Xinduct__1: $i > $i ).
thf(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1: $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1: $i > $i ).
thf(v_sko__List__Xreplicate__Xinduct__1_type,type,
v_sko__List__Xreplicate__Xinduct__1: $i > $i ).
thf(c_Lambda_OdB_OdB__size_type,type,
c_Lambda_OdB_OdB__size: $i > $i ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Lambda_Oliftn_type,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1: $i > $i ).
thf(v_e_____type,type,
v_e____: $i ).
thf(v_T_H_____type,type,
v_T_H____: $i ).
thf(v_sko__List__Xupt__Xinduct__1_type,type,
v_sko__List__Xupt__Xinduct__1: $i > $i ).
thf(c_Type_Otypings_type,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1: $i > $i ).
thf(v_ua_______type,type,
v_ua______: $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i > $i ).
thf(514,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(1879,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(151,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(1024,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(1823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(1729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(176,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1083,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(218,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1179,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(275,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I3_J_0) ).
thf(1322,plain,
! [A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OAbs @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(1665,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(611,axiom,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).
thf(2109,plain,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(620,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(2131,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(2072,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(1767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(1840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ A @ B @ D ) ) @ ( c_Lambda_Oliftn @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(1850,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(264,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(1295,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(1956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( ( c_Power_Opower__class_Opower @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_0) ).
thf(1549,plain,
! [B: $i,A: $i] :
( ( ( c_Power_Opower__class_Opower @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).
thf(1005,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_1) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(613,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(2114,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(609,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(552,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(1793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(173,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1078,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= ( c_Lambda_Oliftn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Lambda_OdB_OdB__size @ B ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I2_J_0) ).
thf(1608,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Lambda_OdB_OdB__size @ A ) ) @ ( c_Lambda_OdB_OdB__size @ B ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(1756,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(578,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(2035,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(643,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) @ ( c_Suc @ D ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ E ) @ C ) ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(2184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) @ ( c_Suc @ D ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ E ) @ C ) ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(563,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1999,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(277,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(1327,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(530,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1919,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlexn__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_0) ).
thf(1954,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xlexn__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(441,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(2141,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( C
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(2168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ C )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ C )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(898,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(138,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(1001,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(403,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(1613,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(1359,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(343,axiom,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(1475,plain,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(638,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(2173,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(1887,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(195,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1127,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
thf(1782,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(841,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(2136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1904,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_1) ).
thf(1228,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(1623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(347,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(1254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(1628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(260,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(1287,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(322,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(1430,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(422,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(1660,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(510,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1871,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1907,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(333,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1455,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(1992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(618,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_6) ).
thf(2126,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(359,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(1511,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1462,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1059,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(531,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1922,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(75,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(853,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1514,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(584,axiom,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2049,plain,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(190,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1115,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1568,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(631,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(2158,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(414,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_2) ).
thf(1641,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1963,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) @ D ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) @ D ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(520,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1890,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(1815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__shift__lb__Suc0__0__upt_0) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(512,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(1875,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1778,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(2007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(640,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2178,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(575,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(2027,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(2090,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ C ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ C ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(280,axiom,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1334,plain,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(1682,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(491,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I1_J_0) ).
thf(1828,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(2017,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1151,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(588,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2058,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(1928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
thf(988,plain,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(608,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2103,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ D ) ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ D ) ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(398,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(1600,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(185,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1104,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(766,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(1896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(645,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(2190,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(2002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(136,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(998,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ A @ tc_nat ) @ ( c_Power_Opower__class_Opower @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__less__imp__less_0) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ C @ A @ tc_nat ) @ ( c_Power_Opower__class_Opower @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ C @ tc_nat ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) ) @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add1__eq_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) ) ) @ ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Divides_Odiv__class_Omod @ A @ C @ tc_nat ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) ) @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
thf(2204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1691,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(325,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1438,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_5) ).
thf(925,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(1306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(634,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) @ D )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ C @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ D @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(2164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) @ D )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ C @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ D @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(615,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(2118,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(2047,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(564,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(2000,plain,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1470,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(2083,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(169,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1067,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(453,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Onchotomy_0) ).
thf(1736,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A )
= B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
thf(1163,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(79,axiom,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(862,plain,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(355,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not0__implies__Suc_0) ).
thf(1502,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(693,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(729,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(119,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(957,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(235,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ A ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I6_J_0) ).
thf(1223,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OAbs @ A ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(384,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ A ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(1570,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ A ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(2147,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(788,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(2015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ A @ C @ D ) ) @ ( c_Lambda_Osubstn @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(318,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1423,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(399,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1602,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(1365,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(551,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(544,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_0) ).
thf(1951,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(1457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
thf(2068,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(641,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(2179,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(174,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_1) ).
thf(1079,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1281,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(411,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1634,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Power_Opower__class_Opower @ B @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__power_0) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Power_Opower__class_Opower @ B @ C @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(649,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(2200,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OBeta_0) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(642,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(2181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(655,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(2211,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(1983,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(1762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(370,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1534,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(1111,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(461,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I6_J_0) ).
thf(1755,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1936,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(373,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__0_0) ).
thf(1541,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(630,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2157,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(468,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(1772,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(857,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(278,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(1329,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(209,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xlexn__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lexn_Oinduct_1) ).
thf(1160,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xlexn__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(753,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1739,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_0) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(519,axiom,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(1889,plain,
! [B: $i,A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(1842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(2038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(2085,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(456,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1744,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(265,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ A ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(1297,plain,
! [A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ A ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(162,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oexhaust_0) ).
thf(1050,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1 @ A ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(130,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(984,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(1799,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(542,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(502,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(1852,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(321,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1429,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(1324,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(189,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(1114,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(1932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(1979,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(779,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(1759,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(504,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1857,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(651,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2203,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(485,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1814,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(242,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__power__eq__Suc__0__iff_2) ).
thf(1241,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(654,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(2208,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(581,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).
thf(2043,plain,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(338,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1466,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(1663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(587,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2057,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(596,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(2076,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(123,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(965,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(639,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(2176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(2149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__decomp_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_1) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(745,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ B @ A @ tc_nat ) ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div__lemma_2) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ B @ A @ tc_nat ) ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(298,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
thf(1374,plain,
! [A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ A ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).
thf(2121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ A ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(2144,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(417,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1648,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(975,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(1007,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(529,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
thf(732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(404,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(1615,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(1652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ C ) @ D @ tc_nat ) @ tc_nat @ A ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ C ) @ D @ tc_nat ) @ tc_nat @ A ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(1965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(633,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(2161,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(1997,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ B @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I5_J_0) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ tc_Lambda_OdB )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ A @ tc_Lambda_OdB ) ) @ ( c_Nat_Osize__class_Osize @ B @ tc_Lambda_OdB ) ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(1638,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(412,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(1635,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(451,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
thf(1733,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(635,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBB @ A @ B @ C @ D @ E @ F )
= ( hAPP @ A @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(2166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBB @ A @ B @ C @ D @ E @ F )
= ( hAPP @ A @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1464,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(114,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(947,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(900,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(311,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1408,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(143,axiom,
! [A: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ A @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(1011,plain,
! [A: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ A @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1524,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(614,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
= ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(2116,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
= ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= C )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(513,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1877,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(574,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(2025,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBC @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(758,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A ) ) @ ( hAPP @ B @ D ) ) )
| ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_1) ).
thf(1557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A ) ) @ ( hAPP @ B @ D ) ) )
| ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(2111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(848,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(1838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(488,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(1820,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
thf(1688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(426,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(1667,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(210,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_a____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_I3_J_0) ).
thf(1162,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_a____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ D @ E @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ E @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(112,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(943,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(149,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
thf(1022,plain,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(342,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1474,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_u____ ) @ v_i____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(1594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(145,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(1015,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_1) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(2101,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(653,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2207,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(922,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
thf(685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(959,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(2171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(768,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ B @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel1_0) ).
thf(2051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(695,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) @ C ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(1775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) @ C ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(137,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(1000,plain,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(2054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(1583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(483,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(1809,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ D ) @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(2096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ D ) @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(316,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(1420,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ B @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
| ~ ( c_Type_Otypings @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(2124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ B @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
| ~ ( c_Type_Otypings @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
thf(1509,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(1472,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(147,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1018,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(1958,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ C @ A @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(219,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(1181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(2005,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1076,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(283,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1340,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(2192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Oliftn @ A @ ( c_Lambda_OdB_OVar @ B ) @ C )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(400,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1605,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(540,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(1941,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(1780,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(776,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(712,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult1__eq_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) @ tc_nat ) ) @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(467,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1770,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(362,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1516,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1598,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(589,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__m_0) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(1484,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(163,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1053,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(475,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(1790,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(331,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1452,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(221,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ B ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ F ) @ D ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ B ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ F ) @ D ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
thf(1785,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(2128,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(1901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1085,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(2044,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self__is__m_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(250,axiom,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(1262,plain,
! [A: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ C ) ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(951,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(388,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1579,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(1934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(1543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(1702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(427,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(1670,plain,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).
thf(1372,plain,
! [A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ B @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(523,axiom,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(1898,plain,
! [B: $i,A: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat )
| ( B = A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct_1) ).
thf(1257,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_u____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Suc @ v_i____ ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ v_u____ ) @ v_i____ ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ v_u____ @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_i____ @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(656,plain,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_u____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_Suc @ v_i____ ) ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ v_u____ ) @ v_i____ ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ v_u____ @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ v_i____ @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(480,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(1802,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(150,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1023,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(391,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ B @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ A @ C @ F @ tc_Type_Otype ) @ D @ E )
| ~ ( c_Type_Otyping @ A @ B @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(1585,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ B @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ C @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ E )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ A @ C @ F @ tc_Type_Otype ) @ D @ E )
| ~ ( c_Type_Otyping @ A @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(200,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(1140,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(576,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(2030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(601,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(1459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(1685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(543,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1949,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(647,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__zero__less__power__iff_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Power_Opower__class_Opower @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(597,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(2078,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(1913,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(313,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
thf(1412,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(329,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1448,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(386,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1575,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(844,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(1734,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(1807,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ A ) @ B @ C )
= ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_Oliftn @ A @ B @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(1674,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(346,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1481,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(1745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(1854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(365,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1523,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) ) @ D ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) ) @ D ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(302,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(1385,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(1062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(357,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ v_r____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
thf(1508,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ v_r____ ) ) @ v_a____ ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_T_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(506,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
thf(1861,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(2081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(2041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
thf(2066,plain,
! [B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(360,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1513,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_0) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(160,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(1045,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(604,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2095,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(521,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(1893,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(270,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
thf(1309,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(1133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(286,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(1348,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1642,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(387,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1578,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(1546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(818,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1380,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(182,axiom,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__if_0) ).
thf(1097,plain,
! [A: $i] :
( ( c_Power_Opower__class_Opower @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) @ A )
= C )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(1303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1527,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(212,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(1165,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(801,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(1989,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(593,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(2070,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubstn @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_Oliftn @ C @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ B @ D @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(155,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ A ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_1) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ C @ ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ A ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_1) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ B @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(740,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(253,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1268,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(1976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(396,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1597,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1299,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(2138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) @ B ) ) )
| ~ ( c_Type_Otyping @ C @ A @ v_T____ )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SI1_0) ).
thf(2159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) @ B ) ) )
| ~ ( c_Type_Otyping @ C @ A @ v_T____ )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r____ ) @ v_a____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_as____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__div__cancel__disj_0) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(1532,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(908,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult2__eq_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Odiv @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(1923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1713,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(1565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(500,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(1848,plain,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(39,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(755,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(178,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1088,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(227,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(1204,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(1944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(1367,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ A ) @ B ) ) )
| ~ ( c_Type_Otyping @ C @ A @ v_T____ )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ v_a____ @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SI2_0) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_a____ ) @ A ) @ B ) ) )
| ~ ( c_Type_Otyping @ C @ A @ v_T____ )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ C @ B @ v_T____ @ tc_Type_Otype ) @ v_a____ @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ) @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult2__eq_0) ).
thf(2074,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ C @ tc_nat ) @ tc_nat ) ) @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(2227,plain,
$false,
inference(e,[status(thm)],[1879,1024,1823,1168,1995,1729,846,1031,1083,941,1179,1554,1322,1665,2109,2131,2072,1767,893,1840,1315,1850,666,1295,1956,1549,1750,1005,683,1618,1939,1073,1205,2114,677,1406,2104,1971,1793,1078,1671,1608,1137,1756,2035,2184,1999,715,1872,1233,1327,1919,1954,1354,930,1497,1705,1275,2141,2168,698,1095,898,1001,885,1613,2010,1645,1359,1475,2173,1529,1887,1243,1127,1782,782,1441,2020,841,2136,1904,1228,1623,1482,1254,1628,724,1287,1430,1660,785,1871,1907,838,1826,1455,1992,2126,949,1511,917,751,1462,1059,1922,853,1514,2049,1479,1013,1115,1568,2158,1641,1963,1319,1890,969,1572,1815,1494,1875,1778,2007,2178,1489,2027,2090,1040,1334,1682,1858,1828,1677,1960,821,2017,1811,1450,1151,937,1383,1020,1581,966,2058,1928,1377,1796,660,988,1433,2103,1201,1600,1104,981,766,1896,877,2190,1119,774,2002,998,2154,1521,1863,2204,1691,1438,925,1306,2164,2118,810,1338,2047,1868,2000,1153,761,1470,2093,2083,1067,1736,1047,798,1163,1343,1519,862,1502,1487,693,2032,729,1387,1723,910,957,1223,1042,952,1570,1174,2133,1217,2147,788,1370,1238,2015,1883,1560,1423,1602,1365,1968,1951,1457,2068,2179,1079,1281,1634,1910,1106,2200,830,1836,1787,2181,1195,2211,1291,710,1592,1983,1762,1534,1064,1111,1587,1425,869,1755,1350,1936,1089,1541,874,2157,1143,1270,1772,1259,857,1397,1329,1160,1361,933,753,1739,1700,1791,1214,1889,706,1414,1842,2038,1446,1016,1207,2085,1155,1744,1263,1099,701,1297,1974,1552,1050,984,721,1799,1947,1852,1429,1246,1720,1324,1114,1266,1831,1192,1932,1979,779,1759,1393,1857,2203,1814,1241,2208,2043,1695,1563,1035,1466,674,1663,1026,794,2057,1054,2076,1170,718,888,1278,965,1251,2176,1146,1698,2149,824,1273,745,1301,1374,1631,2121,2144,906,1135,1648,975,1833,1007,1916,732,1615,1125,1652,743,1535,1403,1965,2161,1707,1312,1865,1997,1332,1092,1638,1635,1733,2166,1765,919,804,1464,947,1209,900,1408,1011,1524,1492,2116,737,880,1122,2197,1589,990,996,1877,2025,758,1557,816,2111,1731,848,1838,1177,1820,1688,890,1667,1162,726,1029,895,943,1022,1293,668,1198,1474,1594,1015,986,2022,1477,2101,1726,1102,2207,922,1805,658,912,685,959,2171,768,827,2051,695,1775,1000,1435,2054,1583,1809,2096,944,680,1420,927,2124,1509,1472,1018,1958,1181,2005,1076,1081,749,939,1340,1845,1070,2192,2012,1605,1941,1780,1753,776,1748,712,1003,1770,690,1516,1598,1225,2060,1400,1230,1484,1053,1790,1452,791,1186,1785,2128,1317,1901,1085,1679,2044,1220,1262,1235,1538,951,1130,1579,1934,1543,703,1702,1284,864,1427,1670,1372,1881,1898,1257,1141,1981,656,1802,1023,1585,978,1140,1717,2030,1421,1649,2088,1459,1685,1949,2194,1108,671,1817,1157,2078,1913,688,903,1654,1412,1448,2187,1189,1390,1575,1289,844,1453,1734,1807,771,963,2098,1674,1481,1745,1854,1523,2152,961,813,1385,1062,1508,1861,2081,914,2041,2066,1212,763,1513,1661,1444,1045,2095,832,1893,1309,1116,1133,1348,1642,1578,1546,818,1380,1248,867,735,1097,835,1395,1625,854,1303,1986,1527,1148,1363,1657,807,1165,955,796,1742,2201,801,1989,1335,1693,2070,1172,1410,1056,664,1033,1710,1346,2063,1610,1930,740,1829,1268,1976,1357,1925,1597,1299,1885,871,2138,2159,1352,1532,860,908,992,1500,1923,850,1713,1505,1621,1565,1848,1037,755,1088,1204,2106,1468,708,882,1944,1367,935,1009,1184,2074,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 15:53:49 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.69/1.06 % [INFO] Parsing done (217ms).
% 1.69/1.07 % [INFO] Running in sequential loop mode.
% 2.22/1.26 % [INFO] eprover registered as external prover.
% 2.22/1.26 % [INFO] cvc4 registered as external prover.
% 2.29/1.26 % [INFO] Scanning for conjecture ...
% 2.64/1.38 % [INFO] Found a conjecture and 656 axioms. Running axiom selection ...
% 3.12/1.50 % [INFO] Axiom selection finished. Selected 654 axioms (removed 2 axioms).
% 3.74/1.66 % [INFO] Problem is propositional (TPTP CNF).
% 3.74/1.67 % [INFO] Type checking passed.
% 3.74/1.68 % [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 ...
% 11.19/3.45 % External prover 'e' found a proof!
% 11.19/3.45 % [INFO] Killing All external provers ...
% 11.19/3.45 % Time passed: 2927ms (effective reasoning time: 2376ms)
% 11.19/3.45 % 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)>
% 11.19/3.45 % Axioms used in derivation (654): cls_mult__eq__1__iff_1, cls_Nil__is__map__conv_1, cls_shift__commute_0, cls_add__0__left_0, cls_subst__lt_0, cls_natgb_Oadd__r0__iff_1, cls_subst__map_0, cls_dB_Osimps_I6_J_0, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_nat_Oinduct_0, cls_power__0_0, cls_dvd__mult__cancel1_0, cls_nat__dvd__not__less_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_mult__cancel2_0, cls_add__is__1_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_nat__dvd__1__iff__1_1, cls_of__nat__add_0, cls_dvd_Oantisym__conv_0, cls_nat__mult__eq__1__iff_1, cls_Suc__inject_0, cls_dvd__mult2_0, cls_subst__App_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, cls_Var__eq__apps__conv_1, cls_of__nat__0_0, cls_mod__mult__mult1_0, cls_subst__eq_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_add__less__cancel__left_1, cls_dvd__mult__right_0, cls_setsum__head__upt__Suc_0, cls_one__is__add_4, cls_nat__1__eq__mult__iff_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__is__0_2, cls_upt_Oinduct_1, cls_liftn_Osimps_I1_J_1, cls_left__add__mult__distrib_0, cls_COMBC__def_0, cls_mult__less__cancel__right__disj_0, cls_dB_Osimps_I8_J_0, cls_sum__squares__eq__zero__iff_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_mult__less__cancel__left__disj_1, cls_nat__mult__div__cancel__disj_0, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_less__antisym_0, cls_CHAINED_0, cls_less__add__Suc2_0, cls_of__nat__less__iff_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_mod__by__0_0, cls_add__is__1_2, cls_power__inject__exp_0, cls_mod__mod__cancel_0, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_liftn_Osimps_I2_J_0, cls_nat__mod__eq__iff_1, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, cls_div__add__self2_0, cls_nat__mult__dvd__cancel1_0, cls_uIT_0, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_not__less__eq_1, cls_nat__add__left__cancel__less_0, clsarity_nat__Orderings_Olinorder, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_mod__add__left__eq_0, cls_split__mod_1, cls_less__Suc__eq_2, cls_dvd__div__mult__self_0, cls_one__is__add_1, cls_dvd__1__iff__1_1, cls_appR_0, cls_SI2_0, cls_zero__induct_1, cls_mod__mult__self1__is__0_0, cls_class__ringb_Onoteq__reduce_0, cls_lift__subst__lt_0, cls_split__div_H_6, cls_power__one_0, cls_power__gt1_0, cls_Suc__mult__cancel1_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_add__cancel__21_1, cls_mod__div__equality_0, cls_nat__mult__1_0, cls_div__mult__self1__is__m_0, cls_listsp_ONil_0, cls_nat__power__eq__Suc__0__iff_1, cls_mod__mult__right__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_substn_Osimps_I1_J_2, cls_of__nat__0__less__iff_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_lexn_Oinduct_0, cls_power__less__imp__less__exp_0, cls_natgb_Oadd__mul__solve_0, cls_mult__less__cancel1_0, cls_beta_0, cls_div__by__0_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_split__div_5, cls_subst__preserves__beta_0, cls_mult__Suc__right_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_gr0I_0, cls_lift__type_0, cls_mod__add__self2_0, cls_mult__less__cancel2_1, cls_add__gr__0_0, cls_Nil__is__map__conv_0, cls_mult__less__cancel__right__disj_3, cls_mult__eq__0__iff_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_nat__less__cases_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_zero__less__double__add__iff__zero__less__single__add_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_add__less__mono_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_setsum__shift__lb__Suc0__0__upt_0, cls_n__less__n__mult__m_0, cls_nat__mult__eq__cancel1_0, cls_mod__by__1_0, cls_class__semiring_Omul__0_0, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, clsarity_nat__Divides_Osemiring__div, cls_setsum__op__ivl__Suc_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_not0__implies__Suc_0, cls_div__mult2__eq_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_Beta_I1_J_0, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, cls_mult__pos__neg_0, cls_nat__0__less__mult__iff_0, cls_of__nat__power_0, cls_div__mult__self2__is__id_0, cls_shift__eq_0, cls_mult__eq__1__iff_0, cls_mult__strict__right__mono_0, cls_substn__subst__n_0, cls_mult__dvd__mono_0, cls_div__self_0, cls_liftn__0_0, cls_div__mult__mult1_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_dvd__mult__cancel2_1, cls_dB_Osimps_I3_J_0, cls_mod__div__trivial_0, cls_foldl__absorb0_0, cls_dvd__mult__cancel__right_2, cls_add__Suc_0, cls_power__Suc2_0, cls_subst__Var_2, cls_dvd__mult__div__cancel_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_lexn_Oinduct_1, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_xt1_I10_J_0, cls_mod__add__cong_0, cls_mult__is__0_1, cls_dvd_Oless__le__trans_1, cls_add__less__cancel__right_1, cls_mult__less__cancel2_2, cls_nat__add__left__commute_0, cls_mod__mult__self1_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_nat_Oinducts_0, cls_one__is__add_5, cls_power__gt1__lemma_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_mod__lemma_0, cls_no__zero__divisors_0, cls_lift__lift_0, cls_div__mult__div__if__dvd_0, cls_ATP__Linkup_OCOMBC__def_0, cls_div__add__self1_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, cls_nat__zero__less__power__iff_0, cls_nat__mult__dvd__cancel__disj_0, cls_mod__div__equality2_0, cls_mult__neg__pos_0, cls_of__nat__1_0, cls_div__1_0, cls_class__semiring_Osemiring__rules_I2_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_App__eq__foldl__conv_0, cls_dvd__imp__mod__0_0, cls_mod__Suc_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_combine__common__factor_0, cls_dB_Osimps_I4_J_0, cls_typing__elims_I1_J_0, cls_mult__pos__neg2_0, cls_Suc__neq__Zero_0, cls_nat__mult__1__right_0, cls_add__is__1_0, cls_power__eq__0__iff_2, cls_map__is__Nil__conv_0, cls_div__mod__equality2_0, cls_class__ringb_Onoteq__reduce_1, cls_power__mult_0, cls_liftn_Osimps_I3_J_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__less__cancel__left__disj_0, cls_dvd__trans_0, cls_class__semiring_Oadd__a_0, cls_dB_Osize_I5_J_0, cls_mod__mult__left__eq_0, cls_one__is__add_0, cls_less__add__Suc1_0, cls_dvd__1__iff__1_0, cls_Var__IT_0, cls_dvd__mult__cancel_0, cls_dvd__1__left_0, cls_dvd__mod__iff_1, cls_class__semiring_Osemiring__rules_I19_J_0, cls_add__right__cancel_0, cls_dvd__reduce_1, cls_dvd_Oeq__iff_0, cls_div__mult__self1_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_power__less__power__Suc_0, cls_comm__monoid__add_Omult__commute_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_nat__mult__div__cancel__disj_1, cls_zero__less__mult__pos_0, cls_nat__power__eq__Suc__0__iff_2, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_of__nat__eq__iff_0, cls_mult__less__cancel1_1, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_replicate_Oinduct_0, cls_nat__add__assoc_0, cls_zero__less__two_0, cls_less__add__one_0, cls_class__ringb_Oadd__mul__solve_0, cls_dvd_Oless__le__trans_0, cls_power__strict__decreasing_0, cls_natgb_Onoteq__reduce_1, cls_dvd__antisym_0, cls_of__nat__0__less__iff_1, cls_One__nat__def_0, cls_dvd__triv__right_0, cls_ATP__Linkup_OCOMBB__def_0, cls_add__strict__mono_0, cls_nat__mult__dvd__cancel1_1, cls_div__less__dividend_0, cls_sum__squares__eq__zero__iff_1, cls_lessI_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, cls_Abs__App__neq__Var__apps_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_uT_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_class__semiring_Omul__d_0, cls_natgb_Oadd__scale__eq__noteq_0, cls_dB_Osimps_I1_J_0, cls_dvd__div__mult_0, cls_apps__eq__Abs__conv_2, cls_lift__map_0, cls_add__cancel__21_0, cls_nat__induct_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_less__Suc__eq__0__disj_3, cls_dvd__add_0, cls_nat__1__eq__mult__iff_2, cls_less__add__eq__less_0, cls_nat_Onchotomy_0, cls_split__mod_0, cls_lift_Osimps_I3_J_0, cls_mod__mult__self4_0, cls_dB_Osize_I3_J_0, cls_mod__mult__cong_0, cls_no__zero__divirors__neq0_0, cls_mult__Suc_0, cls_div__by__1_0, cls_replicate_Oinduct_1, cls_power__Suc_0, cls_dvd__reduce_0, cls_natgb_Oadd__cancel_0, cls_zero__neq__one_0, cls_split__div_1, cls_dvd__refl_0, cls_of__nat__mult_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_div__mult__self__is__m_0, cls_nat_Oexhaust_0, cls_dvd__mult__cancel__left_2, cls_subst__Var_1, cls_mod__Suc_1, cls_power__Suc__0_0, cls_dvd__mult__cancel__right_1, cls_neq0__conv_1, cls_nat__mult__dvd__cancel__disj_1, cls_less__1__mult_0, cls_Suc__mult__less__cancel1_1, cls_one__is__add_2, cls_apps__eq__Abs__conv_1, cls_dB_Osize_I4_J_0, cls_mult__less__cancel__right__disj_5, cls_mod__mult__self2_0, cls_mult__is__0_0, cls_dvd_Oless__trans_1, cls_add__less__cancel__right_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, clsarity_nat__Orderings_Opreorder, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_mod__mult__distrib2_0, cls_nat_Oinducts_1, cls_Suc__times__mod__eq_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_subst__lemma_0, clsarity_nat__Ring__and__Field_Odvd, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_foldl__assoc_0, cls_class__semiring_Osemiring__rules_I28_J_0, cls_lifts__IT_0, cls_class__semiring_Omul__1_0, cls_SI1_0, cls_div__less_0, cls_mod__1_0, cls_dvd__mod_0, cls_Var__apps__neq__Abs__apps_0, cls_Beta_I6_J_0, cls_less__not__refl_0, cls_div__mod__equality_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_nat__zero__less__power__iff_1, cls_gr0__conv__Suc_1, cls_mod__0_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, cls_mult__cancel1_1, cls_linorder__neqE__ordered__idom_0, cls_class__semiring_Opwr__pwr_0, cls_div__dvd__div_0, cls_div__add_0, cls_add__mult__distrib_0, cls_dvd__triv__left_0, cls_class__ringb_Oadd__cancel_0, cls_dvd_Oless__le_0, cls_mod__add__self1_0, cls_dB_Osimps_I2_J_1, cls_class__semiring_Osemiring__rules_I3_J_0, cls_mult__eq__0__iff_2, cls_nat__1__eq__mult__iff_1, cls_sum__squares__gt__zero__iff_1, cls_subst__subst_0, cls_natgb_Onoteq__reduce_0, cls_mult__less__mono1_0, clsarity_nat__Ring__and__Field_Osemiring, cls_Beta_I3_J_0, cls_mod__mod__trivial_0, cls_mult__strict__left__mono__comm_0, cls_class__ringb_Oadd__r0__iff_0, cls_linorder__neq__iff_1, cls_mult__less__cancel__left__neg_1, cls_nat_Oinject_0, cls_add__lessD1_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_dvd__power_1, cls_one__dvd_0, cls_linorder__less__linear_0, cls_mult__less__mono2_0, cls_power__mult__distrib_0, cls_div__0_0, cls_liftn__lift_0, cls_map__is__Nil__conv_1, cls_dvd__mod__iff_0, cls_power__strict__increasing__iff_1, cls_substn_Osimps_I2_J_0, cls_not__less__less__Suc__eq_1, cls_class__semiring_Opwr__Suc_0, clsarity_nat__Power_Opower, cls_class__semiring_Osemiring__rules_I11_J_0, cls_Nat_Oadd__0__right_0, cls_dvd_Ole__less__trans_1, cls_nat__mult__eq__1__iff_2, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_lift_Osimps_I1_J_1, cls_Suc__lessD_0, cls_nat__neq__iff_0, cls_mult__less__cancel__left__pos_1, cls_split__div_0, cls_natgb_Oadd__r0__iff_0, cls_add__is__1_4, cls_add__is__1_5, cls_power__commutes_0, cls_dvd__mult__cancel2_0, cls_add__neg__neg_0, cls_dB_Osize_I1_J_0, cls_trans__less__add2_0, cls_nat__power__less__imp__less_0, cls_nat__mult__less__cancel1_1, cls_power__add_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_dvd__mult__cancel__left_1, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__less__cancel2_0, cls_less__Suc0_0, cls_dvd_Ole__neq__trans_0, cls_div__power_0, cls_div__mult__self2_0, cls_div__mult1__eq_0, cls_typing_OVar_0, cls_mult__less__cancel__left__disj_3, cls_lift__IT_0, cls_nat__mult__div__cancel1_0, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mult__less__cancel1_2, cls_mod__mult__self2__is__0_0, cls_add__mult__distrib2_0, cls_abs_0, cls_mod__add__right__eq_0, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_sum__squares__eq__zero__iff_2, cls_Abs__eq__apps__conv_2, cls_zero__less__mult__pos2_0, cls_nat__induct_1, cls_n__less__m__mult__n_0, cls_mult__1_0, cls_IT_OVar_0, cls_mod__mult__mult2_0, cls_mod__mult__eq_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_mult__1__left_0, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_mult__less__cancel__right__disj_4, cls_power__one__right_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_trans__less__add1_0, cls_class__semiring_Osemiring__rules_I35_J_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, cls_dvd_Oeq__iff_2, cls_dvd__mult__cancel__right_0, cls_comm__monoid__add_Omult__1_0, cls_liftn_Osimps_I1_J_0, cls_nat__mult__eq__1__iff_0, cls_div__mult__mult2_0, cls_dvd__mult__cancel1_1, cls_order__less__irrefl_0, cls_mod__mult__self3_0, cls_dvd_Oorder__trans_0, cls_add__is__0_2, cls_power__eq__0__iff_0, cls_Abs__eq__apps__conv_0, cls_div__add1__eq_0, cls_one__less__power_0, cls_power__Suc__less__one_0, cls_dvd_Oneq__le__trans_0, cls_add__is__1_3, cls_apps__preserves__beta_0, cls_dvd_Oless__trans_0, cls_class__semiring_Osemiring__rules_I27_J_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_App__eq__foldl__conv_4, cls_dvd__0__right_0, cls_class__semiring_Oadd__c_0, cls_mult__pos__pos_0, cls_nat__add__left__cancel_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_split__mod_5, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_nat__mult__dvd__cancel__disj_2, cls_nat__zero__less__power__iff_2, cls_zmod__simps_I1_J_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_less__SucI_0, cls_div__if_0, cls_substn_Osimps_I1_J_1, cls_power__eq__if_0, cls_sum__squares__gt__zero__iff_0, cls_dvd_Oantisym_0, cls_dvd__power_0, cls_nat__0__less__mult__iff_2, cls_not__less0_0, cls_mod__div__decomp_0, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_subst__Abs_0, cls_subst__Var__IT_0, cls_shift__gt_0, cls_div__dvd__div_1, cls_one__is__add_3, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_mult__less__cancel__left__disj_2, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_nat__mult__assoc_0, cls_substn_Osimps_I3_J_0, cls_dB_Osimps_I5_J_0, cls_dvdI_0, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, cls_mult__eq__self__implies__10_0, cls_foldl__Nil_0, cls_Suc__less__eq_0, cls_mult__eq__0__iff_1, cls_add__gr__0_2, cls_lift_Osimps_I1_J_0, cls_nat__power__eq__Suc__0__iff_0, cls_mult__cancel1_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_IT_OBeta_0, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_dvd__mod__imp__dvd_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_div__mult__self1__is__id_0, cls_add__gr__0_1, cls_dvd__mult_0, cls_mod__eq__0__iff_1, cls_power__strict__increasing__iff_0, cls_upt_Oinduct_0, cls_div__mult__mult1__if_0, cls_less__Suc0_1, cls_subst__lift_0, cls_nat__dvd__1__iff__1_0, cls_termination__basic__simps_I2_J_0, cls_of__nat__Suc_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_dB_Osize_I6_J_0, cls_Abs__eq__apps__conv_1, cls_mod__mult2__eq_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_mult__idem_0, cls_lift__types_0, cls_dB_Osize_I2_J_0, cls_split__div__lemma_2, cls_mod__if_0, cls_semiring__div__class_Omod__div__equality_H_0, cls_substs__lemma_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, cls_class__semiring_Omul__pwr_0, cls_setsum__op__ivl__Suc_1, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_nat__less__le_1, cls_zero__induct_0, cls_natgb_Oadd__mul__solve_1, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, cls_mod__self_0, cls_dB_Osimps_I9_J_0, cls_T_0, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_appL_0, cls_dvd_Ole__less__trans_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_power__Suc__less_0, cls_nat_Oinduct_1, cls_power__0__left_1, cls_mod__Suc__eq__Suc__mod_0, cls_mult__eq__1__iff_2, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_dvd__0__left_0, cls_mod__mult__distrib_0, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1
% 11.19/3.45 % No. of inferences in proof: 1311
% 11.58/3.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2927 ms resp. 2376 ms w/o parsing
% 12.37/3.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.37/3.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------