TSTP Solution File: LCL778-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL778-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:31:38 EDT 2023
% Result : Unsatisfiable 10.68s 3.51s
% Output : Refutation 11.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 654
% Syntax : Number of formulae : 1204 ( 281 unt; 105 typ; 0 def)
% Number of atoms : 2493 ( 748 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 16034 (1314 ~;1394 |; 0 &;13326 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 105 usr; 16 con; 0-6 aty)
% Number of variables : 3658 ( 0 ^;3658 !; 0 ?;3658 :)
% 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(v_s_type,type,
v_s: $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(v_ss_type,type,
v_ss: $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(v_i_type,type,
v_i: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_Orderings_Oord__class_Omax_type,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $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(c_ListOrder_Ostep1_type,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(c_List_Ofoldr_type,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $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(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(c_OrderedGroup_Osemigroup__add_type,type,
c_OrderedGroup_Osemigroup__add: $i > $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_Transitive__Closure_Ortranclp_type,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_Groebner__Basis_Ogb__semiring_type,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
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_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(c_Type_Otypings_type,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(c_Type_Osko__Type__Xvar__app__typesE__1__1_type,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_OrderedGroup_Omonoid__add_type,type,
c_OrderedGroup_Omonoid__add: $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Lambda_OdB_OdB__case_type,type,
c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $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(v_sko__InductTermi__XIT__Xcases__4_type,type,
v_sko__InductTermi__XIT__Xcases__4: $i > $i ).
thf(v_sko__InductTermi__XIT__Xcases__5_type,type,
v_sko__InductTermi__XIT__Xcases__5: $i > $i ).
thf(v_sko__InductTermi__XIT__Xcases__6_type,type,
v_sko__InductTermi__XIT__Xcases__6: $i > $i ).
thf(v_sko__InductTermi__XIT__Xcases__3_type,type,
v_sko__InductTermi__XIT__Xcases__3: $i > $i ).
thf(v_sko__InductTermi__XIT__Xcases__2_type,type,
v_sko__InductTermi__XIT__Xcases__2: $i > $i ).
thf(v_sko__InductTermi__XIT__Xcases__1_type,type,
v_sko__InductTermi__XIT__Xcases__1: $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3_type,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4_type,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1_type,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2_type,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2: $i > $i ).
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(c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2_type,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1_type,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__Xlem__1__3_type,type,
c_ListApplication_Osko__ListApplication__Xlem__1__3: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__Xlem__1__4_type,type,
c_ListApplication_Osko__ListApplication__Xlem__1__4: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__Xlem__1__1_type,type,
c_ListApplication_Osko__ListApplication__Xlem__1__1: $i > $i ).
thf(c_ListApplication_Osko__ListApplication__Xlem__1__2_type,type,
c_ListApplication_Osko__ListApplication__Xlem__1__2: $i > $i ).
thf(c_List_Olistsum_type,type,
c_List_Olistsum: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(c_Lambda_OdB_OdB__rec_type,type,
c_Lambda_OdB_OdB__rec: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_type,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(c_Lambda_OdB_OdB__size_type,type,
c_Lambda_OdB_OdB__size: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_Lambda_Oliftn_type,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_type,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(c_Type_Osko__Type__Xvar__app__types__1__1_type,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
thf(329,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1322,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1036,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)],[209]) ).
thf(444,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
= ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(1586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D @ E )
= ( c_List_Oreplicate @ B @ ( hAPP @ A @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(1718,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)],[500]) ).
thf(394,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1469,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(272,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1190,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)],[272]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(505,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(1729,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(1237,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(909,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)],[154]) ).
thf(549,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(1840,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)],[549]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(1315,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)],[325]) ).
thf(268,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(1179,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)],[268]) ).
thf(316,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1295,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1110,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)],[240]) ).
thf(43,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(645,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Olist_OCons @ B @ D @ F ) @ ( c_List_Olist_OCons @ A @ C @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(892,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)],[147]) ).
thf(431,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1559,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(238,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ D @ A @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I33_J_0) ).
thf(1105,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ D @ A @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(1211,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)],[281]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem_3) ).
thf(1596,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(416,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(1522,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1569,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)],[437]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(1073,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)],[225]) ).
thf(279,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(1205,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(1591,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)],[446]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1269,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)],[305]) ).
thf(141,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( C = B )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(878,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( C = B )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(1437,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)],[381]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(401,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_7) ).
thf(1486,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D )
= ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D )
= ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(537,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_4) ).
thf(1808,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(1705,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)],[494]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(1608,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)],[453]) ).
thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(1655,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)],[473]) ).
thf(516,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(1756,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(5,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(550,plain,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(1735,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)],[507]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(715,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)],[72]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(1275,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)],[307]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(1260,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(1640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
thf(1063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1354,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1078,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)],[227]) ).
thf(528,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(1788,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)],[528]) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(1761,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)],[518]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(913,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)],[155]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(1746,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(1001,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1613,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)],[455]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1386,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)],[359]) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(1529,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)],[419]) ).
thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(829,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)],[120]) ).
thf(233,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1095,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)],[233]) ).
thf(294,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(1243,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(181,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(973,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)],[181]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1046,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)],[213]) ).
thf(471,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(1650,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)],[471]) ).
thf(468,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(1645,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(1518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(493,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(1703,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1287,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)],[312]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_OrderedGroup_Omonoid__add @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__left_0) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_OrderedGroup_Omonoid__add @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(1577,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)],[440]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(934,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)],[164]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1059,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)],[219]) ).
thf(334,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(1330,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1264,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)],[303]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(1323,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)],[330]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(124,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(1511,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)],[411]) ).
thf(67,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(702,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( c_ListOrder_Ostep1 @ E @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(1313,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)],[324]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1279,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)],[309]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_OrderedGroup_Omonoid__add @ C @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__right_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_OrderedGroup_Omonoid__add @ C @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(534,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/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1800,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)],[534]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(638,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1087,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)],[230]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(1013,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)],[199]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(1100,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)],[236]) ).
thf(289,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ C @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(1232,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ C @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(179,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ B ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ F @ G @ E @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(969,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ B ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ F @ G @ E @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(606,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(438,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(1572,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)],[438]) ).
thf(510,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(1741,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)],[510]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(881,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(924,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)],[159]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(756,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)],[87]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1373,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)],[353]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(1632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(544,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(1828,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)],[544]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(937,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)],[165]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(1489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1415,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)],[372]) ).
thf(538,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(1811,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)],[538]) ).
thf(386,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_5) ).
thf(1450,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1020,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)],[202]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(574,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(215,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1051,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(981,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(692,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)],[63]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(956,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(362,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1394,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)],[362]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(1526,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)],[418]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(1345,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)],[341]) ).
thf(367,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_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(1405,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_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(277,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ A ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(1201,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)],[277]) ).
thf(450,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(1600,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(1564,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(1622,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)],[459]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(942,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)],[167]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(488,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ F @ G )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(1691,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ C @ D @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ F @ G )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ E ) @ F @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(321,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ E ) @ D ) )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(1306,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ E ) @ D ) )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(810,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(337,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1338,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(495,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(1708,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(1783,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)],[526]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1311,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)],[323]) ).
thf(521,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(1768,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Apps__dB__induct_5) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(1580,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)],[441]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(514,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(1751,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)],[514]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(630,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(1560,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)],[432]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(894,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(340,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(1343,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(266,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(1174,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)],[266]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(561,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(477,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/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1666,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)],[477]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(916,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)],[156]) ).
thf(350,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ F @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(1365,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ F @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(429,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1555,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(1687,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( 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)],[486]) ).
thf(541,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(1819,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(1159,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)],[260]) ).
thf(547,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(1836,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(551,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(710,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(126,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(842,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_ListOrder_Ostep1 @ C @ A @ B @ D )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(566,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)],[10]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(548,axiom,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_6) ).
thf(1837,plain,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(1195,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)],[274]) ).
thf(368,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(1407,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(1634,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)],[464]) ).
thf(361,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(1392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OVar @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(365,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1402,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(650,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)],[45]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(1328,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)],[333]) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1498,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)],[406]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(1425,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)],[377]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(1672,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)],[480]) ).
thf(196,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(1006,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(1138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OVar @ D ) @ E )
= ( hAPP @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(610,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(189,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(989,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1397,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)],[363]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(254,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(1143,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(530,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ 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/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1794,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ 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)],[530]) ).
thf(436,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(1567,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(1361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( c_Lambda_OdB_OAbs @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(4,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(554,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1182,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)],[269]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(529,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ E @ E )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldl @ A @ C @ D @ E @ E ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_0) ).
thf(1791,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ E @ E )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldl @ A @ C @ D @ E @ E ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(590,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)],[20]) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1039,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)],[210]) ).
thf(511,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 @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(1744,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 @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1419,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)],[374]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(1292,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)],[314]) ).
thf(163,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(933,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(1739,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)],[509]) ).
thf(390,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(1461,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(226,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(1075,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(1478,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)],[398]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1297,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)],[317]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1192,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)],[273]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(721,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)],[74]) ).
thf(533,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1799,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(569,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(499,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( B = E )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(1715,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( B = E )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(501,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(1720,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1114,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)],[242]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(1588,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)],[445]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(985,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)],[187]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(1539,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)],[423]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1456,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)],[388]) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(1382,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)],[357]) ).
thf(304,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ E @ A @ F @ C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(1266,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ E @ A @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(545,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(1831,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(1333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(380,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(1434,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)],[380]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(1318,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)],[327]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(539,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_8) ).
thf(1814,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(293,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_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(1241,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_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(476,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/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(1663,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)],[476]) ).
thf(413,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(1515,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1054,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)],[217]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1466,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)],[392]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem_5) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(271,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ B @ A @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(1187,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ B @ A @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(953,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)],[172]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1185,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)],[270]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(1754,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)],[515]) ).
thf(491,axiom,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1698,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)],[491]) ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(1548,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)],[426]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(856,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)],[132]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(319,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1301,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(251,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(1135,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(470,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_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(1648,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_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(177,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_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(965,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_lessequals @ ( 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)],[177]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(1727,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)],[504]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oreplicate @ B @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oreplicate @ B @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(546,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(1833,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ E ) @ E ) @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(458,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(1620,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)],[458]) ).
thf(531,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(1795,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)],[531]) ).
thf(415,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(246,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(1124,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(1226,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)],[287]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(182,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(975,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)],[182]) ).
thf(456,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(1615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1389,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)],[360]) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(958,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)],[174]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(1403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(1428,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(408,axiom,
! [A: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(1503,plain,
! [A: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(12,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_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(572,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_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(352,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1371,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)],[352]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(157,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(919,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(1258,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)],[300]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1356,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)],[346]) ).
thf(520,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1765,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)],[520]) ).
thf(231,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(1090,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(1464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(947,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)],[170]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(604,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)],[25]) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(1408,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)],[369]) ).
thf(310,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(1282,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1349,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)],[343]) ).
thf(424,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ B @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(1542,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ B @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1122,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)],[245]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(439,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(1574,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)],[439]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(1011,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)],[198]) ).
thf(190,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(990,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(192,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(996,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(1492,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)],[404]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(1603,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)],[451]) ).
thf(522,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ C ) @ E ) )
= ( hAPP @ ( hAPP @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ B @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(1771,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ C ) @ E ) )
= ( hAPP @ ( hAPP @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ B @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(354,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ F ) ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(1376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ D ) @ E ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ F ) ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(462,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1630,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)],[462]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(700,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)],[66]) ).
thf(331,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1325,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1029,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)],[206]) ).
thf(256,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(1149,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(626,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(1177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E )
= ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(241,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(1112,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1339,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)],[338]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(2,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(552,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ v_r ) @ v_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(1556,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)],[430]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(769,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(1171,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)],[265]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(983,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)],[186]) ).
thf(200,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_1) ).
thf(1015,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(608,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)],[27]) ).
thf(158,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(922,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(536,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ E @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(1805,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ E @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1562,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)],[433]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1213,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)],[282]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
thf(827,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ E @ D ) @ ( c_List_Oappend @ C @ E @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(212,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_11) ).
thf(1044,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
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 ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1066,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)],[222]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(1445,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)],[384]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(1034,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)],[208]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( 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)],[168]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(663,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)],[50]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(927,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)],[160]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(1684,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)],[485]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1081,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)],[228]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldl @ A @ C @ D @ E @ E ) )
= ( c_List_Ofoldl @ A @ B @ D @ E @ E ) )
| ~ ( c_OrderedGroup_Omonoid__add @ C @ A @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add_Ofoldl__absorb0_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldl @ A @ C @ D @ E @ E ) )
= ( c_List_Ofoldl @ A @ B @ D @ E @ E ) )
| ~ ( c_OrderedGroup_Omonoid__add @ C @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(3,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(553,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(517,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(1758,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)],[517]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1166,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)],[263]) ).
thf(278,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(1203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ B @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(1208,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)],[280]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1145,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ 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)],[255]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ ( hAPP @ C @ D ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(1400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ ( hAPP @ C @ D ) @ ( c_Lambda_OdB_OdB__rec @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(144,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(887,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(452,axiom,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_9) ).
thf(1605,plain,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1368,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)],[351]) ).
thf(525,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 @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(1780,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 @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(1484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OdB__case @ A @ B @ C @ ( c_Lambda_OdB_OAbs @ D ) @ E )
= ( hAPP @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(1748,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)],[513]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(712,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)],[71]) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(1003,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)],[195]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(690,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1611,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)],[454]) ).
thf(497,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ A @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
thf(1711,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ A @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(465,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/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(1637,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)],[465]) ).
thf(111,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(808,plain,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(42,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_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(643,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_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(285,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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(1220,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)],[285]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(527,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ C @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(1785,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ C @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1262,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)],[302]) ).
thf(290,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(1235,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ B @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_OCons @ E @ B @ D ) @ ( c_List_Olist_OCons @ F @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(326,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1317,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(1763,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)],[519]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(576,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)],[14]) ).
thf(474,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(1658,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(1285,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)],[311]) ).
thf(508,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1738,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(1358,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)],[347]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(1536,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)],[422]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(613,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(1052,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)],[216]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1008,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)],[197]) ).
thf(306,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(1272,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(140,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(876,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1617,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)],[457]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(535,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(1802,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)],[535]) ).
thf(203,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(1023,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_ListOrder_Ostep1 @ A @ D @ E @ F )
| ~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(443,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(1585,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1140,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)],[253]) ).
thf(479,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_10) ).
thf(1670,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(1797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(845,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)],[127]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(229,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(1084,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(1459,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)],[389]) ).
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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(556,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(162,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/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(931,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)],[162]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(1553,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)],[428]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(1412,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)],[371]) ).
thf(283,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_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(1216,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_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(385,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(1448,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Lambda_OdB_OdB__case @ B @ C @ D @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ E ) @ F ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(94,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(771,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(671,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)],[54]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(1817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[183]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(688,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)],[61]) ).
thf(313,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(1289,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1453,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)],[387]) ).
thf(469,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/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(1646,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)],[469]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(963,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)],[176]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1476,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)],[397]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Apps__dB__induct_3) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ A ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(481,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_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(1674,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_lessequals @ 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)],[481]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(1481,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(169,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(946,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(632,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(542,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/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1822,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)],[542]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(1523,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)],[417]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(588,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( 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)],[298]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(961,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)],[175]) ).
thf(358,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(1385,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(220,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1062,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(410,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(1508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_ListOrder_Ostep1 @ C @ ( c_List_Olist_OCons @ B @ D @ E ) @ ( c_List_Olist_OCons @ A @ F @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(403,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1491,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(1689,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)],[487]) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1777,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)],[524]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1513,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)],[412]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1309,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)],[322]) ).
thf(261,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(1161,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(52,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(667,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(315,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1294,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(1440,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)],[382]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(1133,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)],[250]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(999,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)],[193]) ).
thf(523,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(1774,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(1725,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)],[503]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(1678,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)],[483]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(967,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)],[178]) ).
thf(288,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ E @ F @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(1229,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ E @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(1625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( 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)],[467]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(950,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)],[171]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(447,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_2) ).
thf(1593,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ A @ ( c_List_Oappend @ B @ C @ D ) @ ( c_List_Oappend @ B @ E @ D ) @ D )
| ~ ( c_ListOrder_Ostep1 @ A @ C @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1303,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)],[320]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1248,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)],[296]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(790,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(801,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)],[108]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(1495,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)],[405]) ).
thf(218,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(1056,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(1473,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)],[396]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(336,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(1335,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(489,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(1693,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(1410,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)],[370]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(496,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(1710,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(1197,plain,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(188,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(987,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)],[188]) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(1352,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)],[344]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(1129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(420,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(1532,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)],[420]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(1550,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)],[427]) ).
thf(407,axiom,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_0) ).
thf(1500,plain,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(498,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(1713,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E )
= ( c_List_Omap @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(379,axiom,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_Ocases_3) ).
thf(1431,plain,
! [A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ A ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ A ) ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ A ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1299,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)],[318]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1505,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)],[409]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( 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)],[244]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(803,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(1320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(1653,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)],[472]) ).
thf(484,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(1681,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(676,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(393,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1468,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(223,axiom,
! [A: $i] :
( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ A ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__head__tail_0) ).
thf(1069,plain,
! [A: $i] :
( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ A ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(48,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(659,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(435,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(180,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(972,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1842,plain,
$false,
inference(e,[status(thm)],[1322,1036,1586,1718,1469,1190,760,1729,1237,909,1840,1315,1179,1295,1110,645,892,1559,1105,1211,582,1596,683,1522,1569,1073,1205,1591,1269,878,1437,861,1486,1443,1808,1705,1608,1655,1756,550,1735,715,1275,814,1260,1640,1063,1354,1078,1788,1761,747,913,1746,1001,1613,1386,1529,829,1095,1243,1127,973,1046,1650,1645,1518,1703,724,1287,1660,1577,934,1059,1330,1264,1323,619,838,1511,702,1313,1279,1545,559,1800,638,1087,1013,1100,1232,969,606,1347,1572,1741,881,924,756,1373,1632,834,1828,937,1489,1415,1811,1450,1020,574,1051,821,981,1169,634,692,956,1394,1526,1345,1405,1201,1600,849,1696,1564,1622,774,942,678,1691,661,1306,1199,810,1338,1708,1783,1311,1768,798,1163,1723,778,1042,1580,1255,1751,630,788,1560,1223,894,825,1343,1174,1676,561,1666,1423,916,1365,1555,665,1687,1819,1159,1836,1027,551,710,842,847,566,1032,1837,1195,1407,1634,1392,1402,697,650,615,1328,1498,1425,1672,1006,1138,593,869,610,989,1397,742,578,874,1143,1534,1794,1567,884,1361,554,1182,1700,1791,590,1039,1744,1419,1292,933,1739,1461,901,686,1075,1478,1297,1668,1192,721,1799,569,1715,1720,1627,1825,1114,1588,985,1539,1456,1382,1266,1831,1131,654,1333,1434,1318,792,1814,1241,805,1663,1515,1732,765,1054,1466,1071,1187,674,953,1185,794,586,718,888,1251,1754,1698,1548,856,745,1301,733,601,1135,1648,965,750,1727,1154,819,1833,772,1620,1795,1520,1124,1226,904,975,1615,1389,958,1403,1428,1503,572,1371,1239,919,1258,1356,1765,1090,1464,947,604,1408,1282,1048,1349,1542,1122,784,1117,1574,1011,990,996,1492,1603,1771,737,599,1376,890,1471,816,1630,621,700,1325,1029,1149,626,668,1177,1112,758,1339,858,552,1556,769,1171,983,1015,608,922,1805,1562,1213,827,695,1245,636,1044,1066,1445,851,1102,1034,1583,944,680,663,927,1684,1277,648,1081,617,939,754,553,823,836,1758,1166,1203,1208,1145,1018,580,640,1025,1400,887,1605,739,1368,1780,1484,1098,993,776,1748,712,1003,690,1598,705,1611,1711,1637,808,643,1220,907,840,1785,1262,1235,1317,1763,576,1658,1285,1738,1218,1358,1536,613,1052,864,727,1008,1272,876,1617,656,1802,1023,1585,978,1140,1670,1797,845,1421,1084,1459,556,931,1553,1157,1412,1216,1448,771,1108,671,1817,976,688,1289,1453,1646,1326,963,1476,1341,1674,1481,946,632,1822,1523,781,588,1253,961,1385,1062,1508,731,786,1491,1689,1777,763,1513,899,832,1309,1161,667,1294,1440,929,1133,999,1774,1725,1678,967,1229,1625,867,1642,752,950,1097,1593,1380,854,1303,1248,790,564,801,1363,1495,1056,1473,796,1335,1693,897,1410,767,1710,1197,987,1352,1129,1152,1532,1550,1500,1713,1431,1299,871,1505,1120,1093,624,596,1378,803,1320,1653,1681,676,1468,1069,708,659,1565,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL778-1 : TPTP v8.1.2. Released v4.1.0.
% 0.17/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n026.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 16:31:36 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.66/1.11 % [INFO] Parsing done (216ms).
% 1.66/1.11 % [INFO] Running in sequential loop mode.
% 2.28/1.33 % [INFO] eprover registered as external prover.
% 2.28/1.34 % [INFO] cvc4 registered as external prover.
% 2.28/1.34 % [INFO] Scanning for conjecture ...
% 2.66/1.47 % [INFO] Found a conjecture and 544 axioms. Running axiom selection ...
% 3.09/1.61 % [INFO] Axiom selection finished. Selected 544 axioms (removed 0 axioms).
% 3.97/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 3.97/1.80 % [INFO] Type checking passed.
% 3.97/1.81 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.68/3.50 % External prover 'e' found a proof!
% 10.68/3.50 % [INFO] Killing All external provers ...
% 10.68/3.50 % Time passed: 2965ms (effective reasoning time: 2385ms)
% 10.68/3.50 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.68/3.51 % Axioms used in derivation (544): cls_Nil__is__map__conv_1, cls_semigroup__add__class_Oaxioms_0, cls_not__one__less__zero_0, cls_dB_Osplit_0, cls_dB_Orecs_I1_J_0, cls_add__0__left_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_natgb_Oadd__r0__iff_1, cls_subst__map_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_zero__less__one_0, cls_gb__semiring_Osemiring__rules_I33_J_0, cls_power__0_0, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_of__nat__add_0, cls_add__less__cancel__left_1, cls_IT_Ocases_4, cls_gb__semiring_Omul__0_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_IT_Ocases_7, cls_gb__semiring_Osemiring__rules_I12_J_0, cls_of__nat__0_0, cls_gb__semiring_Osemiring__rules_I7_J_0, cls_subst__eq_0, cls_class__ringb_Oadd__r0__iff_1, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_Cons__step1__Cons_0, cls_liftn_Osimps_I1_J_1, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_map__replicate_0, cls_append__self__conv_0, cls_dB_Osimps_I8_J_0, cls_subject__reduction_0, cls_Apps__dB__induct_5, cls_zero__le__one_0, cls_min__max_Ole__sup__iff_2, cls_termi__implies__IT_0, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_append__step1I_0, cls_replicate__empty_0, cls_conversepD_0, cls_liftn_Osimps_I2_J_0, cls_of__nat__less__iff_0, cls_Cons__eq__map__conv_3, clsarity_fun__Orderings_Oorder, cls_class__semiring_Osemiring__rules_I20_J_0, cls_accp__downwards_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_monoid__add_Ofoldl__absorb0_0, cls_power__inject__exp_0, cls_linorder__neqE_0, cls_listsum_Osimps_I1_J_0, cls_add__strict__right__mono_0, cls_pos__add__strict_0, cls_monoid__add_Oadd__0__left_0, cls_add__le__cancel__left_1, cls_rtrancl__beta__Abs_0, cls_IT_Ocases_10, cls_Snoc__step1__SnocD_2, cls_add__is__0_0, cls_not__Cons__self2_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_gb__semiring_Osemiring__rules_I3_J_0, cls_IT_Ocases_0, cls_add__le__cancel__right_1, clsarity_nat__Orderings_Olinorder, cls_termination__basic__simps_I1_J_0, cls_substn__subst__0_0, cls_nat__add__left__cancel__less_0, cls_dB_Osimps_I12_J_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_comm__monoid__add_Omult__1__right_0, cls_lift__subst__lt_0, cls_power__one_0, cls_dB_Osplit__asm_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_add__left__cancel_0, cls_power__less__imp__less__exp_0, cls_append__eq__Cons__conv_4, cls_add__nonpos__neg_0, cls_le__maxI2_0, cls_eq__Nil__appendI_0, cls_comm__monoid__add_Omult__assoc_0, cls_substn_Osimps_I1_J_2, cls_of__nat__0__less__iff_0, cls_rtranclp__trans_0, cls_Cons__step1__Cons_5, cls_add__cancel__21_1, cls_same__append__eq_0, cls_gb__semiring_Osemiring__rules_I13_J_0, cls_head__Var__reduction_1, cls_beta_0, cls_append__Cons_0, cls_listsum__append_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_subst__preserves__beta_0, cls_less__max__iff__disj_2, cls_foldl__foldr1_0, cls_add__nonneg__pos_0, cls_replicate__eq__replicate_0, cls_gr0I_0, cls_lift__type_0, cls_add__gr__0_0, cls_Nil__is__map__conv_0, cls_add__is__0_1, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_less__max__iff__disj_0, cls_dB_Orecs_I3_J_0, cls_gb__semiring_Oadd__c_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_foldr_Osimps_I1_J_0, cls_nat__less__cases_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_order__less__asym_0, cls_add__right__mono_0, cls_add__less__mono_0, cls_gb__semiring_Omul__c_0, cls_append1__eq__conv_1, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_listsum_Osimps_I2_J_0, cls_order__eq__refl_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_Apps__dB__induct_3, cls_gb__semiring_Omul__d_0, cls_linorder__antisym__conv2_0, cls_lem_5, cls_order__le__less_0, cls_shift__eq_0, cls_linorder__antisym__conv1_0, cls_semigroup__add_Oadd__assoc_0, cls_substn__subst__n_0, cls_liftn__0_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_gb__semiring_Osemiring__rules_I16_J_0, cls_dB_Osimps_I3_J_0, cls_gb__semiring_Osemiring__rules_I14_J_0, cls_replicate__append__same_0, cls_foldl__absorb0_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_max__0R_0, clsarity_bool__Orderings_Oorder, cls_subst__Var_2, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_le__maxI1_0, cls_append__Nil2_0, cls_add__less__cancel__right_1, cls_nat__add__left__commute_0, cls_append__self__conv2_0, cls_min__max_Osup__least_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_Var__eq__apps__conv_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_dB_Osimps_I11_J_0, cls_Nil__is__append__conv_0, cls_add__left__mono_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_min__max_Ole__supE_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_min__max_Ole__sup__iff_1, cls_gb__semiring_Osemiring__rules_I9_J_0, cls_gb__semiring_Omul__1_0, cls_add__strict__left__mono_0, cls_App__eq__foldl__conv_0, cls_of__nat__0__le__iff_0, cls_self__append__conv2_1, cls_dB_Osimps_I4_J_0, cls_Cons__step1__Cons_1, cls_of__nat__1_0, cls_IT_Ocases_8, cls_self__append__conv2_0, cls_min__max_Osup__left__idem_0, cls_map__eq__Cons__conv_3, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_add__less__mono1_0, cls_typing__elims_I1_J_0, cls_append__is__Nil__conv_2, cls_gb__semiring_Osemiring__rules_I25_J_0, cls_map__is__Nil__conv_0, cls_le__max__iff__disj_1, cls_append__eq__append__conv2_5, cls_Var__IT_0, cls_Cons__step1__Cons_3, cls_append__in__listsp__conv_1, cls_subject__reduction_H_0, cls_var__app__typesE_1, cls_power__eq__0__iff_2, cls_append__Nil_0, cls_class__semiring_Oadd__a_0, cls_append__in__listsp__conv_0, cls_gb__semiring_Osemiring__rules_I21_J_0, cls_append__eq__Cons__conv_5, cls_liftn_Osimps_I3_J_0, cls_converse__rtranclp__into__rtranclp_0, cls_min__max_Oless__supI1_0, cls_add__right__cancel_0, cls_xt1_I8_J_0, cls_apps__preserves__betas_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_IT_Ocases_11, cls_of__nat__eq__iff_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_comm__monoid__add_Omult__commute_0, cls_foldl__Cons_0, cls_gb__semiring_Osemiring__rules_I5_J_0, cls_dB_Osimps_I10_J_0, cls_Snoc__step1__SnocD_3, cls_gb__semiring_Osemiring__rules_I17_J_0, cls_class__semiring_Oadd__0_0, clsarity_nat__Nat_Osemiring__char__0, cls_replicate__app__Cons__same_0, cls_power__strict__mono_0, cls_zero__less__two_0, cls_min__max_Ole__supI_0, cls_add__strict__mono_0, cls_not__add__less1_0, cls_power__strict__decreasing_0, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_replicate__eq__replicate_1, cls_head__Var__reduction_0, cls_of__nat__0__less__iff_1, cls_IT__implies__termi_0, cls_not__leE_0, cls_min__max_Osup__idem_0, cls_less__add__one_0, cls_zero__less__power_0, cls_order__antisym_0, cls_order__trans_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__add__eq__less_0, cls_max__less__iff__conj_2, cls_append__step1I_1, cls_IT_Ocases_3, cls_not__Cons__self_0, cls_conversep__conversep_0, cls_lift_Osimps_I3_J_0, cls_dB_Osimps_I1_J_0, cls_self__append__conv_1, cls_apps__eq__Abs__conv_2, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_lift__map_0, cls_add__cancel__21_0, cls_linorder__antisym__conv1_1, cls_append__same__eq_0, clsarity_bool__Orderings_Opreorder, cls_Cons__step1__Cons_2, cls_rtrancl__beta__AppL_0, cls_Nil__is__append__conv_1, cls_Nitpick_Ortranclp__def_1, cls_monoid__add_Oadd__0__right_0, cls_zero__neq__one_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_gb__semiring_Osemiring__rules_I8_J_0, cls_subst__Var_1, cls_IT_Ocases_2, cls_natgb_Oadd__cancel_0, cls_neq__Nil__conv_1, cls_neq0__conv_1, cls_linorder__not__le_1, cls_append__assoc_0, cls_not__Nil__step1_0, cls_foldr_Osimps_I2_J_0, cls_dB_Osize_I4_J_0, cls_add__less__cancel__right_0, cls_listsum_0, cls_lift__preserves__beta_0, cls_apps__eq__Abs__conv_1, cls_min__max_Ole__sup__iff_0, cls_lifts__IT_0, clsarity_nat__Orderings_Opreorder, cls_not__less__iff__gr__or__eq_1, cls_order__le__neq__trans_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_Var__apps__neq__Abs__apps_0, cls_max__0L_0, cls_subst__lemma_0, cls_gb__semiring_Osemiring__rules_I10_J_0, cls_foldl__assoc_0, cls_order__eq__iff_2, cls_less__not__refl_0, cls_append__in__listsp__conv_2, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_gb__semiring_Osemiring__rules_I2_J_0, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_less__le__not__le_1, cls_dB_Osimps_I2_J_1, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_foldl__foldr1__lemma_0, cls_Cons__step1__Cons_4, cls_linorder__antisym__conv3_0, cls_conversep_Ointros_0, cls_linorder__neqE__ordered__idom_0, cls_map__append_0, cls_add__nonneg__eq__0__iff_1, cls_accp__downwards__aux_0, cls_var__app__types_1, cls_add__nonneg__nonneg_0, cls_empty__replicate_0, cls_dB_Osplit__asm_2, cls_min__max_Osup__absorb1_0, cls_order__antisym__conv_0, cls_add__lessD1_0, cls_gb__semiring_Osemiring__rules_I6_J_0, cls_even__less__0__iff_1, cls_lift__preserves__beta_H_0, cls_order__neq__le__trans_0, cls_power__eq__imp__eq__base_0, cls_IT_Ocases_9, cls_class__ringb_Oadd__r0__iff_0, cls_foldr__append_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_replicate__add_0, cls_gb__semiring_Omul__pwr_0, cls_gb__semiring_Osemiring__rules_I22_J_0, cls_add__strict__increasing_0, cls_power__strict__increasing__iff_1, cls_max__less__iff__conj_1, cls_substn_Osimps_I2_J_0, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_rtranclp_Ortrancl__refl_0, cls_Nat_Oadd__0__right_0, cls_gb__semiring_Osemiring__rules_I18_J_0, cls_map__is__Nil__conv_1, cls_lift_Osimps_I1_J_1, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_trans__less__add2_0, cls_gb__semiring_Oadd__0_0, cls_natgb_Oadd__r0__iff_0, cls_App__eq__foldl__conv_2, cls_min__max_Ole__supI1_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_xt1_I11_J_0, cls_map_Osimps_I2_J_0, cls_dB_Osize_I1_J_0, cls_IT_Ocases_5, cls_add__neg__neg_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_min__max_Osup__left__commute_0, cls_accp__downward_0, cls_Snoc__step1__SnocD_0, cls_Abs__eq__apps__conv_2, cls_dB_Orecs_I2_J_0, cls_xt1_I6_J_0, cls_rtranclp__idemp_0, cls_append__is__Nil__conv_1, cls_typing_OVar_0, cls_dB_Osplit_1, cls_IT_OVar_0, cls_listsum__foldr_0, cls_abs_0, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_le__add__right__mono_0, cls_min__max_Ole__iff__sup_1, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_gb__semiring_Oadd__a_0, cls_size__char_0, cls_lift__IT_0, cls_replicate__eq__replicate_2, cls_le__max__iff__disj_2, cls_power__one__right_0, cls_trans__less__add1_0, cls_apps__preserves__beta2_0, cls_plus__nat_Oadd__0_0, cls_min__max_Osup__assoc_0, cls_IT_Ocases_1, cls_linorder__not__le_0, cls_Cons__eq__appendI_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_accp_Ocases_0, cls_comm__monoid__add_Omult__1_0, cls_liftn_Osimps_I1_J_0, cls_apps__preserves__beta_0, cls_order__less__irrefl_0, cls_append__is__Nil__conv_0, cls_add__nonneg__eq__0__iff_2, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_append__eq__appendI_0, cls_list_Oinject_1, cls_one__less__power_0, cls_nat__add__left__cancel_0, cls_min__max_Oless__supI2_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_foldr__conv__foldl_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_App__eq__foldl__conv_4, cls_add__is__0_2, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_foldl__append_0, cls_substn_Osimps_I1_J_1, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_le__max__iff__disj_0, cls_semigroup__add_Ofoldl__assoc_0, cls_gb__semiring_Osemiring__rules_I24_J_0, cls_add__neg__nonpos_0, cls_append__replicate__commute_0, cls_not__less0_0, cls_substn_Osimps_I3_J_0, cls_dB_Osimps_I5_J_0, cls_gb__semiring_Osemiring__rules_I19_J_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_add__less__cancel__left_0, cls_shift__gt_0, cls_gb__semiring_Omul__a_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_conversep__eq_0, cls_subst__Abs_0, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_min__max_Ole__iff__sup_0, cls_less__max__iff__disj_1, cls_gb__semiring_Osemiring__rules_I4_J_0, cls_zero__le__power_0, cls_gb__semiring_Osemiring__rules_I20_J_0, cls_max__less__iff__conj_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_dB_Osplit__asm_1, cls_max__add__distrib__left_0, cls_gb__semiring_Opwr__0_0, cls_foldl__Nil_0, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_add__gr__0_2, cls_add__less__le__mono_0, cls_lift_Osimps_I1_J_0, cls_min__max_Ole__supI2_0, cls_order__less__imp__le_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_add__gr__0_1, cls_min__max_Ole__supE_1, cls_lift__types_0, cls_dB_Osplit_2, cls_power__strict__increasing__iff_0, cls_ex__head__tail_0, cls_add__strict__increasing2_0, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_substs__lemma_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_gb__semiring_Opwr__mul_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_lem_3, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_linorder__not__less_1, cls_append1__eq__conv_0, cls_nat__less__le_1, cls_Beta_0, cls_subst__preserves__beta2_H_0, cls_min__max_Osup__commute_0, cls_add__le__cancel__left_0, cls_empty__replicate_1, cls_Snoc__step1__SnocD_1, cls_gb__semiring_Osemiring__rules_I23_J_0, cls_gb__semiring_Osemiring__rules_I11_J_0, cls_xt1_I7_J_0, cls_not__one__le__zero_0, cls_conversep__iff_1, cls_appL_0, cls_IT_Ocases_6, cls_list_Osimps_I2_J_0, cls_rtranclp__converseD_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_conversep_Ocases_0, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_even__less__0__iff_0, cls_gb__semiring_Osemiring__rules_I1_J_0, cls_rtranclp__converseI_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_rtrancl__beta__AppR_0, cls_power__mono_0, cls_of__nat__less__0__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_gb__semiring_Osemiring__rules_I15_J_0, cls_power__0__left_1, cls_add__le__cancel__right_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0, cls_nat__add__commute_0, cls_double__induction__lemma_0
% 10.68/3.51 % No. of inferences in proof: 1099
% 10.68/3.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2965 ms resp. 2385 ms w/o parsing
% 11.98/3.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.98/3.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------