TSTP Solution File: SCT097-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:31 EDT 2023
% Result : Unsatisfiable 19.55s 5.37s
% Output : Refutation 21.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1539
% Syntax : Number of formulae : 2885 ( 435 unt; 194 typ; 0 def)
% Number of atoms : 7366 (1343 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 59343 (4296 ~;4675 |; 0 &;50372 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 377 ( 377 >; 0 *; 0 +; 0 <<)
% Number of symbols : 196 ( 194 usr; 21 con; 0-7 aty)
% Number of variables : 8694 ( 0 ^;8694 !; 0 ?;8694 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_in_type,type,
c_in: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_e_____type,type,
v_e____: $i ).
thf(v_d_____type,type,
v_d____: $i ).
thf(v_F_type,type,
v_F: $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_HOL_OIf_type,type,
c_HOL_OIf: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(v_h_____type,type,
v_h____: $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(v_n_____type,type,
v_n____: $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
thf(v_P_____type,type,
v_P____: $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
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_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $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(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Relation_Osym_type,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
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_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(c_Finite__Set_Osetprod_type,type,
c_Finite__Set_Osetprod: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_type,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_HOL_Osgn__class_Osgn_type,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_type,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add__meet_type,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__join_type,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(v_r_type,type,
v_r: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(t_b_type,type,
t_b: $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(class_Ring__and__Field_Osgn__if_type,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_List_Osko__Recdef__Xtfl__wf__induct__1__1_type,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(v_sko__Transitive__Closure__Xtrancl__Xcases__1_type,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_Lab_____type,type,
v_Lab____: $i ).
thf(v_Lba_____type,type,
v_Lba____: $i ).
thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinduct__1_type,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_type,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(c_List_Osko__Recdef__Xcuts__eq__1__1_type,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(v_sko__Transitive__Closure__Xrtrancl__Xcases__1_type,type,
v_sko__Transitive__Closure__Xrtrancl__Xcases__1: $i > $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinducts__1_type,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1_type,type,
c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(147,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(1718,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)],[147]) ).
thf(23,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(1411,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)],[23]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(2778,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(84,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(1559,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)],[84]) ).
thf(429,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(2412,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)],[429]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(2331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(3172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(340,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(2199,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)],[340]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(94,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(1586,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)],[94]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(1501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(4201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).
thf(9,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(1369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(627,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ ( c_Product__Type_OSigma @ F @ C @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(2889,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ ( c_Product__Type_OSigma @ F @ C @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(189,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(1823,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(2306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Relation_OId @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(3053,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Relation_OId @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(401,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(2341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(683,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(3008,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(2131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(290,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(2072,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)],[290]) ).
thf(1188,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(4062,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(999,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(3666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(1168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ D @ E @ C ) @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
thf(4022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ D @ E @ C ) @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(887,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(3434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(757,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(3167,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ A ) @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(4183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ A ) @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(910,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(3477,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1014,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(3698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(449,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(2463,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)],[449]) ).
thf(219,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(1899,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)],[219]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(958,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(3581,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(1093,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(3863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1078,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(3830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
thf(2595,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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_zero__le__mult__iff_5) ).
thf(1982,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[254]) ).
thf(435,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(2427,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)],[435]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(2480,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(893,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(3449,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1165,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(4015,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(1956,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(134,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(1686,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 @ C @ B @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__pos_1) ).
thf(4166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 @ C @ B @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(715,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(3072,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1267,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(4226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).
thf(1322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(4339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(2808,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(2495,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(1114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(3912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(374,axiom,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(2282,plain,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(863,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(3382,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(2363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1179,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(4043,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(1176,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ C ) @ G ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ F @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ G @ H @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(4037,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ C ) @ G ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ F @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ G @ H @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(2512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(2976,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1340,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(4376,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(651,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(2940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(1596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(2622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(1091,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(3858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
thf(2908,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
thf(2062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(1443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(2776,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(2659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(927,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
thf(3509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(814,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(3285,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(860,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(3377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(700,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ D @ E @ C ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ D @ E @ C ) @ C @ C ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
thf(3040,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ D @ E @ C ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ D @ E @ C ) @ C @ C ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(751,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(3153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ C @ D @ B @ A ) @ C @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Relation_ORange @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(2953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ C @ D @ B @ A ) @ C @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Relation_ORange @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(2590,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(1939,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(3959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(2671,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(1544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
thf(2676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(921,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(3498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(1261,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(4215,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(2380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1060,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(3794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(736,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(3120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(704,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ A ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) )
| ~ ( c_lessequals @ A @ v_n____ @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(3049,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ A ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) )
| ~ ( c_lessequals @ A @ v_n____ @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(2686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(1170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(4026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(976,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(3616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(455,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(2476,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(799,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
thf(3253,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(828,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBB @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C @ tc_nat @ A @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__setsum_0) ).
thf(3313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ tc_nat ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBB @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C @ tc_nat @ A @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(278,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) @ A )
| ~ ( c_lessequals @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(2042,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) @ A )
| ~ ( c_lessequals @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(688,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(3017,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(338,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(2195,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)],[338]) ).
thf(142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__dvd__setprod__subset_0) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(782,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(3217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(4234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1201,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ E ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ C @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__restrict__set_0) ).
thf(4090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ E ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ C @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(3004,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(837,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ B @ C @ D @ A ) @ C @ A @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_1) ).
thf(3332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ B @ C @ D @ A ) @ C @ A @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(743,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ tc_nat ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( ( hAPP @ B @ D )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__eq__0__iff_0) ).
thf(3135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ tc_nat ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( ( hAPP @ B @ D )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(991,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(3649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(853,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(3365,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(2918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1264,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(4220,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).
thf(334,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(2184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1999,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(2316,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(892,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(3446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(443,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(2448,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)],[443]) ).
thf(840,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(3338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(438,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(2434,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)],[438]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(2712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(878,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(3414,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(164,axiom,
! [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_Otimes__class_Otimes @ A ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(1761,plain,
! [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_Otimes__class_Otimes @ A ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1299,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(4294,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(1640,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2580,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(1106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(3895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(2360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(810,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(3276,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(856,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(3370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(1746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(194,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(1835,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)],[194]) ).
thf(982,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(3629,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(942,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ B @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero__iff_2) ).
thf(3545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ B @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(923,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(3502,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(672,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(2985,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(2020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1366,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(471,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(2516,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)],[471]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(2405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
thf(2869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(984,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(3634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_1) ).
thf(2046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(569,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(2763,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)],[569]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(4371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).
thf(35,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(3308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(3947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1217,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ C @ D @ E @ A @ B ) @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(4124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ C @ D @ E @ A @ B ) @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).
thf(1028,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(3730,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(1921,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1253,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(4198,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1107,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(3898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(2082,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(1172,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(4030,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(2067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1313,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(4322,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ C ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(4156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ C ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(1100,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(3880,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(965,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Relation_Osym @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symD_0) ).
thf(3597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Relation_Osym @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(1344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(4386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(2957,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(883,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(3425,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(734,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(3116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(2339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(842,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(3342,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(710,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(3061,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(993,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(3653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1052,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(3776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(722,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(3089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(1992,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(544,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ C @ E @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__Un__Int_0) ).
thf(2703,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ C @ E @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1073,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(3820,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1104,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(3891,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(3248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(776,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ D @ E @ C ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ D @ E @ C ) @ C @ C ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
thf(3204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ D @ E @ C ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ D @ E @ C ) @ C @ C ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(3263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(784,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(3221,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(1147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(3976,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(639,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(2916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(1126,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(3938,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(4348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).
thf(542,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(2698,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)],[542]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(3131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1266,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(4224,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) )
= ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) )
= ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(955,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(3574,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(222,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(1907,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)],[222]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(2501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(204,axiom,
! [B: $i,A: $i] : ( c_Wellfounded_Owf @ ( c_Wellfounded_Omeasure @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__measure_0) ).
thf(1860,plain,
! [B: $i,A: $i] : ( c_Wellfounded_Owf @ ( c_Wellfounded_Omeasure @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(4130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).
thf(941,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
thf(3542,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(876,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(3410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_0) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(1455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(1036,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(3744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(2126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1064,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(3803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(2466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(2745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(493,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(2571,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)],[493]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(2691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(3099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(930,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(3517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(613,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(2857,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__unique_0) ).
thf(2169,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(141,axiom,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(1704,plain,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(906,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(3470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1133,axiom,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(3951,plain,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(1285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(4265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).
thf(1343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(4383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(968,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(3602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(788,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(3231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(1162,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(4008,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1847,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(2829,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(216,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(1892,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)],[216]) ).
thf(902,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(3463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(3374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(1332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(4358,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(281,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(2049,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)],[281]) ).
thf(1243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(4179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(2767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(414,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(2373,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)],[414]) ).
thf(89,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(1572,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)],[89]) ).
thf(1117,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
thf(3919,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(1311,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omlex__prod @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mlex__less_0) ).
thf(4317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omlex__prod @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).
thf(720,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(3084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(827,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(3312,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(1109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(3902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(995,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ C @ E @ F @ F ) ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ H @ H ) ) @ ( c_Pair @ B @ D @ H @ H ) ) @ I ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(3657,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ C @ E @ F @ F ) ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ H @ H ) ) @ ( c_Pair @ B @ D @ H @ H ) ) @ I ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1030,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ C ) ) @ ( c_Wellfounded_Oacc @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Wellfounded_Oacc @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(3734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ C ) ) @ ( c_Wellfounded_Oacc @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Wellfounded_Oacc @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1225,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_1) ).
thf(4141,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1080,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(3835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1303,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Product__Type_OSigma @ E @ F @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(4302,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Product__Type_OSigma @ E @ F @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(2388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(933,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(3524,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(2090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(755,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(3163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(896,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(3453,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(953,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(3569,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ 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_zero__le__divide__iff_5) ).
thf(2335,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ 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)],[398]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(2017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(1317,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(4329,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1142,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(3966,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(2027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(3199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1241,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(4173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(1450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1282,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ A ) @ ( c_Relation_OId__on @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(4258,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ A ) @ ( c_Relation_OId__on @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(2996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(819,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(3295,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(578,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(2782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1159,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__if_1) ).
thf(4001,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(935,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oinv__image @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ ( hAPP @ E @ B ) @ ( hAPP @ E @ C ) @ F @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(3527,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Relation_Oinv__image @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ ( hAPP @ E @ B ) @ ( hAPP @ E @ C ) @ F @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(908,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(3473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(3983,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(623,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(2880,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(1682,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(889,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(3438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(934,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ B @ A @ A ) @ D @ ( tc_prod @ A @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(3525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ B @ A @ A ) @ D @ ( tc_prod @ A @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(1183,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(4050,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(978,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(3621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(644,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__delta_1) ).
thf(2925,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(252,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(1978,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)],[252]) ).
thf(816,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(3290,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(724,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(3093,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1119,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(3923,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(1960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1049,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(3771,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(4162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
thf(1088,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(3851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(2058,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(2861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1020,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(3712,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(458,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(2483,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)],[458]) ).
thf(434,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ D @ E ) @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(2424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ D @ E ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(2772,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__1_H_1) ).
thf(2137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(1351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(588,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_Relation_Ototal__on @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(2804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_Relation_Ototal__on @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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_mult__nonneg__nonneg_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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)],[100]) ).
thf(961,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(3588,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(467,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(2508,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)],[467]) ).
thf(662,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(2964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(411,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(2367,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(2437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(939,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(3537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(1928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1185,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(4055,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(3068,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(1269,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(4230,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(1174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(4033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(3189,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(1033,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(3739,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(925,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(3505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(214,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(1886,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)],[214]) ).
thf(1067,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Relation_OImage @ D @ B @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(3808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Relation_OImage @ D @ B @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(698,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omlex__prod @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ E ) )
| ~ ( c_lessequals @ ( hAPP @ D @ B ) @ ( hAPP @ D @ C ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mlex__leq_0) ).
thf(3036,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omlex__prod @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ E ) )
| ~ ( c_lessequals @ ( hAPP @ D @ B ) @ ( hAPP @ D @ C ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(2002,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1042,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(3756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(2242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(586,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(2799,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(1405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(970,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__Id_0) ).
thf(3606,plain,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(3906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(70,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1521,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(918,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ C @ D @ F @ F ) ) @ ( c_Relation_Oinv__image @ E @ B @ A @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(3492,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( hAPP @ B @ C ) @ ( hAPP @ B @ D ) @ A @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ F @ F ) ) @ ( c_Pair @ C @ D @ F @ F ) ) @ ( c_Relation_Oinv__image @ E @ B @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(2718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(3406,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(343,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(2205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(765,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(3184,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(2884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1197,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(4082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1564,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1863,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(787,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(3229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(3011,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(822,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(3301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(952,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(3567,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
thf(1438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[34]) ).
thf(805,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(3265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(2164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(766,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(3186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1194,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(4076,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(2641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(4059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(944,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ B @ C @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclE_0) ).
thf(3550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ B @ C @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(880,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(3418,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(1604,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(642,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(2922,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(3151,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(726,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( c_Pair @ E @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(3097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( c_Pair @ E @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(894,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(3450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(924,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(3503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(900,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(3459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1314,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(4323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).
thf(637,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(2910,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(1156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ B @ C @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
thf(3995,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ B @ C @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(830,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(3318,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(1047,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__greater_1) ).
thf(3767,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un_0) ).
thf(2232,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1205,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ B @ C @ A ) @ C @ A @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(4100,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ B @ C @ A ) @ C @ A @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(4312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(1730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(1005,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(3679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(15,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1387,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(803,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(3261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1076,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(3827,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(1145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(3972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(2249,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(2541,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(130,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1676,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(319,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(2147,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)],[319]) ).
thf(1278,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(4252,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ 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_mult__right__le__one__le_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ 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)],[55]) ).
thf(1070,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(3814,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1095,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(3867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(92,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(1580,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)],[92]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(2277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(1035,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(3742,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(665,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ C @ B @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
thf(2969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ C @ B @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(1325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(4344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).
thf(1040,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ A ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(3752,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ A ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(3989,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(4128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(792,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(3239,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(789,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(3233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1101,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_1) ).
thf(3884,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(1294,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) ) @ C ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
thf(4284,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) ) @ C ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(2150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1071,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(3816,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(1619,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(4160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(998,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(3664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(929,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(3514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1006,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(3682,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(1053,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(3778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(2015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1180,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(4044,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(1883,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(813,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ B @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero_0) ).
thf(3282,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ B @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(229,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(1920,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(4053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(772,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(3198,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(598,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(2826,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(957,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(3578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(620,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(2872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(1247,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(4187,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(3144,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(1121,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(3926,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(2741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(352,axiom,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(2228,plain,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(1062,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(3799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(525,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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2653,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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1137,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3958,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(2445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1292,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(4280,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(2758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(1149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(3980,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ ( c_Finite__Set_Ocard @ B @ C ) @ ( c_Finite__Set_Ocard @ A @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__seteq_0) ).
thf(3618,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ ( c_Finite__Set_Ocard @ B @ C ) @ ( c_Finite__Set_Ocard @ A @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(515,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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__inf__distrib__right_0) ).
thf(2628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[515]) ).
thf(1068,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(3810,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1039,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(3750,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(846,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(3349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(947,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(3556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1023,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__delta_H_0) ).
thf(3718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1099,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ F @ C @ D @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(3877,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ F @ C @ D @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(967,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(3600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(1457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1316,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(4327,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(1624,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(938,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
thf(3535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(174,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(1787,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1045,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(3763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(2492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(4104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(483,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(2547,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
thf(2344,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(990,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(3647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(1196,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(4080,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(1123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(3931,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Relation_Orefl__on @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(696,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(3033,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(875,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(3408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ A @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(964,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(3595,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(2769,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(1804,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(1375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(862,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(3381,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(4048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1140,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(3963,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(4012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(1143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(3968,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(1360,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(904,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(3467,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(1592,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(2300,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2498,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(3909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(975,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(3615,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(323,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(2157,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)],[323]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId__on @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(2840,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId__on @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(913,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(3482,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(2100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(737,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(3122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(654,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__dividef_0) ).
thf(2946,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) ) @ ( c_Wellfounded_Oacc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(2990,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) ) @ ( c_Wellfounded_Oacc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__insert_0) ).
thf(1794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(1953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(2895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1277,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(4248,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(2709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1970,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(865,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(3386,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(516,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(2631,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)],[516]) ).
thf(552,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Set_Oinsert @ D @ E @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
thf(2724,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Set_Oinsert @ D @ E @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(1203,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(4095,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)],[1203]) ).
thf(1037,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(3746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(791,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_0) ).
thf(3237,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(161,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(1755,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)],[161]) ).
thf(1128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(3941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(519,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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_sum__squares__eq__zero__iff_2) ).
thf(2638,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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)],[519]) ).
thf(1209,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(4109,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(2268,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1263,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(4219,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).
thf(761,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(3176,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(1284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(4263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
thf(2460,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(4333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(2419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(4191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).
thf(770,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(3194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1025,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(3723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(215,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(1889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1567,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1297,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(4291,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).
thf(745,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__divide__distrib_0) ).
thf(3141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1134,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(3952,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(622,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
thf(2877,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(1964,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(238,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(1942,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)],[238]) ).
thf(1290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(4276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).
thf(123,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1659,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(679,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).
thf(3000,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(393,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(2323,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)],[393]) ).
thf(763,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ F @ C @ D @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(3179,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ F @ C @ D @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(779,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__delta_0) ).
thf(3210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1021,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(3714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1027,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(3728,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(618,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(2868,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(4389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).
thf(1310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(4315,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(1424,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(890,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).
thf(3441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(388,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
thf(2312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(684,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(3010,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ 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_divide__le__0__1__iff_1) ).
thf(1414,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ 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)],[24]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(2172,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(304,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
thf(2108,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(2038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(485,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2551,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1001,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Power_Opower__class_Opower @ E @ ( c_Finite__Set_Ocard @ F @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ F ) )
| ~ ( c_Finite__Set_Ofinite @ F @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__gen__delta_1) ).
thf(3671,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Power_Opower__class_Opower @ E @ ( c_Finite__Set_Ocard @ F @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ F ) )
| ~ ( c_Finite__Set_Ofinite @ F @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(669,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(2978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(2472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(3935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(794,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(3242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(973,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(3611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(739,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__if_2) ).
thf(3126,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).
thf(2851,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(4120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(1984,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(2813,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(1874,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(1429,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(1715,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1231,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Nitpick_Orefl_H @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(4152,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Nitpick_Orefl_H @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1016,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ C @ D @ A @ B ) @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Relation_ODomain @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(3703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ C @ D @ A @ B ) @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Relation_ODomain @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(664,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(2968,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(376,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
thf(2450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(647,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(2932,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(915,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Relation_OId__on @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(3486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Relation_OId__on @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(1057,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(3787,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
thf(1539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[76]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(2836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(2845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(709,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(3059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(848,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(3354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(406,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(2355,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1275,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(4244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(2505,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(867,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(3390,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(491,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(2566,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)],[491]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(1799,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1011,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(3692,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(731,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(716,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ D @ B @ A @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
thf(3074,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ D @ B @ A @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(1191,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ G @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( c_Pair @ H @ D @ G @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( c_Pair @ C @ H @ A @ G ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(4069,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ G @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( c_Pair @ H @ D @ G @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( c_Pair @ C @ H @ A @ G ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(2140,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(1199,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(4086,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2756,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(774,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(3201,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(111,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(1627,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)],[111]) ).
thf(413,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__self__if_0) ).
thf(2370,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ 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)],[413]) ).
thf(781,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(3215,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(4361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).
thf(748,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(3147,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(2203,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(812,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(3279,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)],[812]) ).
thf(624,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(2883,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1090,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(3856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(2748,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(425,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2440,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__less_0) ).
thf(2793,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(2662,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(1066,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(3807,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1075,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
thf(3824,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(1228,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(4148,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(785,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(3225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(950,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(3563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1251,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(4195,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).
thf(963,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(3592,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(824,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(3306,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(1158,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(3999,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ D ) ) @ ( c_Pair @ B @ E @ A @ D ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(832,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(3321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(522,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(2645,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)],[522]) ).
thf(882,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(3422,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)],[882]) ).
thf(1083,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(3841,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1160,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(4004,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(1003,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(3675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(4308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(996,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(3660,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(1764,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1342,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(4380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).
thf(701,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(3042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(917,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(3491,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Relation_Osym @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(3985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ D ) )
| ~ ( c_Relation_Osym @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(506,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(2602,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(1013,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(3696,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_Lab____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(4365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).
thf(753,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(3158,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(309,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(2121,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)],[309]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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_split__mult__pos__le_0) ).
thf(2235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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)],[355]) ).
thf(649,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(2936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(1018,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(3707,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(2391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(634,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ B @ C ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__setprod_0) ).
thf(2904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ B @ C ) @ ( c_Finite__Set_Osetprod @ B @ D @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero__iff_0) ).
thf(4354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(2556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(1213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(4116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).
thf(850,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(3358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(2275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(801,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(3257,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(971,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(3607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(718,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
thf(3079,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(1280,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(4256,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1103,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
thf(3888,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(1082,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(3839,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(2734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(3111,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(809,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(3274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(1287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(4269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(1008,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(3686,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(1166,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(4017,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(474,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(2524,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(870,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ C ) ) @ ( c_Wellfounded_Oacc @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Wellfounded_Oacc @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(3396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ C ) ) @ ( c_Wellfounded_Oacc @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Wellfounded_Oacc @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(831,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(3319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(2791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(972,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(3609,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(670,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ B @ D @ A ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(2981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ B @ D @ A ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(2514,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1173,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(4032,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(1108,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(3900,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(899,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(3458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(873,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(3404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(541,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(2695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(1178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(4041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(1226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(4144,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).
thf(857,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ C @ D @ E @ A @ B ) @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(3372,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ C @ D @ E @ A @ B ) @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1034,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(3741,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1323,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(4341,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).
thf(714,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(3070,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(553,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(2727,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(985,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(3636,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(2859,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(2938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Wellfounded_Oacc @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(800,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(3255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(2789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(931,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(3519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(907,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(3472,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__empty_0) ).
thf(2489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(721,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__delta_H_0) ).
thf(3086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(160,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(1752,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)],[160]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(1652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1031,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(3736,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Relation_ODomain @ D @ C @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(3081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Relation_ODomain @ D @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1043,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(3758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1130,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(3945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(808,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(3272,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(1216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ B @ A @ A ) @ D @ ( tc_prod @ A @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(4122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ B @ A @ A ) @ D @ ( tc_prod @ A @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(1701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(962,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(3590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(2716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(969,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(3604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(2827,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(314,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(2134,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)],[314]) ).
thf(966,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(3599,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(660,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(2959,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(780,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(3213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(691,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(3023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(1050,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(3773,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1211,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ B @ C @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
thf(4112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ B @ C @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(1897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(879,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
thf(3416,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(823,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(3304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(2573,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(758,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(3170,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(937,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( 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(3532,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( 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)],[937]) ).
thf(735,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(3118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(349,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(2220,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(1707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(379,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(2293,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)],[379]) ).
thf(705,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
thf(3051,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(628,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(2891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(2308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(3077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(992,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(3651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(836,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Relation_OId__on @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(3330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Relation_OId__on @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(2738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(1229,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(4149,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).
thf(778,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(3208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(1272,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ G @ C @ D @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(4236,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ G @ C @ D @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(3002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(841,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(3340,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(1997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(888,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Osetprod @ A @ D @ C @ tc_nat ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__pos__nat__iff_0) ).
thf(3436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Osetprod @ A @ D @ C @ tc_nat ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1055,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(3783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(1015,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(3700,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
thf(2706,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(723,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(3091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(1464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(2474,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(2510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(293,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(2079,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)],[293]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(1806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(635,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(2906,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(728,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ tc_nat ) )
= ( c_Finite__Set_Osetprod @ ( c_COMBB @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B @ tc_nat @ A @ D ) @ C @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__setprod_0) ).
thf(3101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ tc_nat ) )
= ( c_Finite__Set_Osetprod @ ( c_COMBB @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B @ tc_nat @ A @ D ) @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(2521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(2721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(847,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(3352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(4337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).
thf(534,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(2679,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1268,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__mono_0) ).
thf(4228,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).
thf(983,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
thf(3631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(456,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(798,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(3251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1337,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(4369,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).
thf(752,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(3155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
thf(2229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(2084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(347,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(2214,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)],[347]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(2383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(430,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ E @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
thf(2415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ E @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(699,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(2422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(2774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(3287,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(71,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(1524,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)],[71]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__def_1) ).
thf(2097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(807,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omeasure @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__measure_1) ).
thf(3270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Wellfounded_Omeasure @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ D @ B ) ) @ ( hAPP @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(375,axiom,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(2284,plain,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_0) ).
thf(1933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(2955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(730,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(3106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(905,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(3468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(77,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) @ F ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ F ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(1542,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) @ F ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ F ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(1722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(4139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(2943,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1260,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(4213,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).
thf(1193,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(4073,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1232,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(4154,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(587,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(2802,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(1242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__timesf_0) ).
thf(4176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).
thf(922,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(3500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(744,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(3138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(2378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(712,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(3066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(3182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(2197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(3160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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_mult__nonpos__nonpos_0) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[333]) ).
thf(592,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2812,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(305,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(2111,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)],[305]) ).
thf(1189,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
thf(4064,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(223,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(1909,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(769,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(3192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1300,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(4296,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(3583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(83,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(1556,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)],[83]) ).
thf(667,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(2974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(188,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1820,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(898,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) ) @ ( c_Wellfounded_Oacc @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(3456,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) ) @ ( c_Wellfounded_Oacc @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(2180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(3219,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(2824,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ C @ D @ A ) @ D @ A @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(1256,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(4203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2605,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(693,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D @ A @ A @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(3027,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D @ A @ A @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(742,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(3133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(1163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(4009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(2314,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1000,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(3668,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(514,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(2625,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(2780,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(1171,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ C @ D @ E @ F @ G @ B @ A ) @ D @ A @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( c_Pair @ C @ D @ G @ B ) ) @ ( c_Relation_Orel__comp @ E @ F @ G @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(4028,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ C @ D @ E @ F @ G @ B @ A ) @ D @ A @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( c_Pair @ C @ D @ G @ B ) ) @ ( c_Relation_Orel__comp @ E @ F @ G @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(756,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Relation_OImage @ D @ B @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(3165,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Relation_OImage @ D @ B @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(1258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ C @ D @ B @ A ) @ C @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Relation_ORange @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(4208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ C @ D @ B @ A ) @ C @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Relation_ORange @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).
thf(1244,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(4181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(697,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(3034,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(428,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) ) ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(2410,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ~ ( class_Ring__and__Field_Ocomm__ring @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) ) ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(579,axiom,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(2785,plain,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(2593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(682,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(3006,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(821,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(3298,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(621,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(2874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(645,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
thf(2928,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(1381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(2842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
thf(2578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(1688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(912,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(3480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(1396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(2365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(2765,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(3917,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1009,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
thf(3687,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(2288,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(4304,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).
thf(344,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(2207,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)],[344]) ).
thf(940,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(3539,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
thf(2075,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1270,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(4232,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(2350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(139,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(1699,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)],[139]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(2212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(981,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(3627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(1339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__delta_H_1) ).
thf(4373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(1643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(412,axiom,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(2369,plain,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1002,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(3674,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1135,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(3953,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(793,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(3241,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(2797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
thf(2244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(517,axiom,
! [E: $i,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_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
thf(2633,plain,
! [E: $i,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_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(826,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__pos_0) ).
thf(3310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(834,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(3325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ A @ C @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ A @ B @ C @ C ) ) @ D ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1252,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(4196,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(928,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(3512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(1293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(4282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(1112,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(3908,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(2693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1234,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(4158,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(1562,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Product__Type_OSigma @ E @ F @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(4084,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Product__Type_OSigma @ E @ F @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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_split__mult__pos__le_1) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ 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)],[263]) ).
thf(1318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(4331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(1948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(183,axiom,
! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(1809,plain,
! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(884,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( c_Pair @ E @ B @ C @ D ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( c_Pair @ E @ A @ C @ D ) ) @ F ) )
| ~ ( c_Relation_Osingle__valued @ F @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(3427,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( c_Pair @ E @ B @ C @ D ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( c_Pair @ E @ A @ C @ D ) ) @ F ) )
| ~ ( c_Relation_Osingle__valued @ F @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(529,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(2665,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(818,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(3293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1118,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ D @ E @ C ) @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
thf(3921,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ D @ E @ C ) @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ B @ C @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(897,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(3455,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(2899,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(1087,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(3849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(891,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(3444,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf_0) ).
thf(2239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(695,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
thf(3031,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ A @ B @ t_a @ t_a ) ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).
thf(1583,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(4136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(2614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(1467,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(2994,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(869,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(3395,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(777,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(3206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(2503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(310,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(2124,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(1312,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_2) ).
thf(4319,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(1990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(2684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(2333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ( ( c_Finite__Set_Osetprod @ E @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ E @ B @ D @ A ) ) @ ( c_Finite__Set_Osetprod @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__Un__disjoint_0) ).
thf(2256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ( ( c_Finite__Set_Osetprod @ E @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ E @ B @ D @ A ) ) @ ( c_Finite__Set_Osetprod @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(2564,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(811,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(3278,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(504,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(2597,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(1958,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1320,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(4336,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1239,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(4168,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(2582,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(954,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_Finite__Set_Osetsum @ C @ A ) @ D @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBC @ D @ B @ C @ A ) @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ F ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
thf(3571,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_Finite__Set_Osetsum @ C @ A ) @ D @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBC @ D @ B @ C @ A ) @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ F ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(2298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
thf(4035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(926,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(3507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1084,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(3842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(2192,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1041,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(3754,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1079,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(3833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(2518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(1097,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(3872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(609,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).
thf(2850,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(1181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B )
!= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(4045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B )
!= ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(652,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Relation_OId @ A ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).
thf(2942,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Relation_OId @ A ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1032,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(3737,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(859,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(3376,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ B @ C @ A ) ) @ ( c_Wellfounded_Oacc @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(3640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ B @ C @ A ) ) @ ( c_Wellfounded_Oacc @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Wellfounded_Oacc @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(99,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(1598,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(1611,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(2375,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(2060,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(156,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
thf(1743,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(3904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(556,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(2732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(901,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(3462,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1254,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(4200,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ C @ B @ A ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(3129,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ C @ B @ A ) ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1132,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
thf(3949,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(4287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(1780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(596,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__delta_0) ).
thf(2821,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( hAPP @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(2407,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(708,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(3058,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(2386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1309,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4314,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
thf(2092,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(1072,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(3818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(1167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ C @ D @ A ) @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(4020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ C @ D @ A ) @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(946,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ v_P____ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PW_0) ).
thf(3554,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ v_P____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(843,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(3344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(994,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(3655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(1329,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(4351,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)],[1329]) ).
thf(1048,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(3769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(2468,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(1237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(4164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(2656,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(3019,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(492,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2569,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(796,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(3246,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(988,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(3642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1326,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(4346,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(256,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
thf(1987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1127,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(3940,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(115,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(1637,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)],[115]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(2688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(838,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(3334,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1059,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(3791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(711,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ E @ B @ A @ A ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ F @ C @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ F @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Finite__Set_Ofinite @ F @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__cases_0) ).
thf(3063,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ E @ B @ A @ A ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ F @ C @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ F @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Finite__Set_Ofinite @ F @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(641,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(2920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(775,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(3202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(1265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(4222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(1869,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(909,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ C @ D @ E @ F @ A @ G @ B ) @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( c_Pair @ C @ D @ A @ G ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ B @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(3475,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ C @ D @ E @ F @ A @ G @ B ) @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( c_Pair @ C @ D @ A @ G ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ B @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(436,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(2429,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1074,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(3823,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Relation_OId @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(2337,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1063,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(3801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(1980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1051,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(3774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1077,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(3828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1221,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(4132,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(2701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(2486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__delta_1) ).
thf(4241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_fequal @ B ) @ B @ B @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ E @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1086,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(3847,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ODomain @ C @ A @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(979,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(3623,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(131,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(1679,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)],[131]) ).
thf(877,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(3412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(3174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(2044,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(725,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(3095,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(1089,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(3853,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1766,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(866,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(3388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1139,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(3961,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(10,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(1372,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)],[10]) ).
thf(854,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ B @ C @ D @ D ) ) @ ( c_Wellfounded_Omeasure @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__measure_0) ).
thf(3366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ A @ B ) ) @ ( hAPP @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ B @ C @ D @ D ) ) @ ( c_Wellfounded_Omeasure @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(4150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).
thf(1210,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(4111,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(1007,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(3684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(4057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(1849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(2838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(488,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(2558,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)],[488]) ).
thf(1144,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(3970,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(3124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(1222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(4133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(675,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(2992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(75,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(1536,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)],[75]) ).
thf(1276,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(4246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(849,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(3356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(373,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(2279,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)],[373]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(2145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1208,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(4106,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)],[1208]) ).
thf(1202,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(4093,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(655,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(2949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(3943,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(1286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(4267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).
thf(2030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1324,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(4342,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(589,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(2807,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(1115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(3914,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2584,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(1281,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(4257,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(871,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ B @ C @ D @ D ) ) @ E ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(3398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ B @ C @ D @ D ) ) @ E ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(1262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ C ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).
thf(4217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ C ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1617,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(292,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(2078,plain,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2347,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(345,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(2209,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)],[345]) ).
thf(1061,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_0) ).
thf(3797,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(1421,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(911,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(3478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(886,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(3433,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
thf(4289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).
thf(1291,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__greater_0) ).
thf(4278,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(895,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(3452,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(2458,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(951,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Relation_Osingle__valued @ D @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(3565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ C @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ B @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( c_Relation_Osingle__valued @ D @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(872,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(3401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(43,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(1459,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)],[43]) ).
thf(1315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(4325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(2310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
thf(1844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(767,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(3188,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(943,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ C @ D @ A @ B ) @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Relation_ODomain @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(3548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ C @ D @ A @ B ) @ A @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ ( c_Relation_ODomain @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(509,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(2611,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(1246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__induct_1) ).
thf(4185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).
thf(980,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(3625,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(1195,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(4078,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1026,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__1_H_0) ).
thf(3725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1 @ C @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(1448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(4102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) @ D ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(2187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) @ D ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(844,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(3346,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1161,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(4006,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(384,axiom,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(2305,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(1240,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(4170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(1575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(707,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(3056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(2643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1866,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(1122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(3929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1734,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(4310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(903,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(3465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(974,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ ( c_Relation_Oconverse @ E @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(3613,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ ( c_Relation_Oconverse @ E @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(673,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(2988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(2167,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(2174,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(914,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(3484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(864,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_3) ).
thf(3383,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(839,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(3336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(4126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).
thf(1038,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(3748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(666,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ B @ C @ D @ A ) @ C @ A @ A ) ) @ D ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_1) ).
thf(2971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ B @ C @ D @ A ) @ C @ A @ A ) ) @ D ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(202,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(1854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(3368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(2443,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(1674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1058,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(3789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(612,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).
thf(2855,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1019,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(3709,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(611,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(2853,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(378,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
thf(2290,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(362,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(2251,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(2532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__infinite_0) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(729,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(3104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ E @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ E @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(1154,axiom,
! [A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id_0) ).
thf(3991,plain,
! [A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(949,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(3561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(2608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(790,axiom,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(3235,plain,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(2431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(997,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(3662,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(1054,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ D @ B @ A @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
thf(3780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ A ) @ C @ A @ ( tc_fun @ A @ A ) @ B ) @ D @ B @ A @ A ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(2934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(2262,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Relation_Oirrefl @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
thf(4261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ B @ A @ A ) ) @ C ) )
| ~ ( c_Relation_Oirrefl @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(2394,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(3978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(1012,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(1298,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(4293,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(2399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ C ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(3149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ C ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ B ) @ ( c_Wellfounded_Oacc @ D @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(936,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(3529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(1607,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
thf(2902,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(2095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(1204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(4098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(1044,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(3761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(1085,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(3844,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(523,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(2648,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(3585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(885,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).
thf(3430,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(3267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(1302,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
thf(4299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).
thf(1004,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(3677,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(2162,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1155,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(3993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(1513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(2036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(989,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ C @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ B ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ C @ A @ B @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).
thf(3645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ C @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ B ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ C @ A @ B @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(1994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(4306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).
thf(945,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(3552,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(881,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(3420,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_1) ).
thf(1614,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(2930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1017,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(3705,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1212,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(4114,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(1105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(3892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(1546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1152,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).
thf(3987,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(1081,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ C @ B @ A ) @ B @ A @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(3837,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ C @ B @ A ) @ B @ A @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(656,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
thf(2951,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(932,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(3521,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ A ) @ ( c_Relation_OId @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1010,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(3690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(1336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(4367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).
thf(317,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(2142,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)],[317]) ).
thf(861,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(3379,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_1) ).
thf(4039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(2,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(1348,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1092,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(3860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1056,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(3785,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(322,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(2155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1341,axiom,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(4378,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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__sup__distrib__right_0) ).
thf(2534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[478]) ).
thf(817,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__less_1) ).
thf(3291,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(1157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(3997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(671,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(2983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(1094,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(3865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(1279,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(4254,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).
thf(1029,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(3733,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(500,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2587,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(2815,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(558,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(2736,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)],[558]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(1757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(1331,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(4357,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(920,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(3496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(3015,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1227,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(4146,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(835,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(3328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(2201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(7,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(1363,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)],[7]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(3347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(3177,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1098,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(3875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(431,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(2417,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)],[431]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(2040,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(2668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(3045,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(1,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1346,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_e____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(2549,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(747,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__def_0) ).
thf(3145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ D ) ) @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ E @ D ) @ D @ D ) ) @ E ) )
| ~ ( c_Wellfounded_Owf @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(2636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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_zero__le__mult__iff_4) ).
thf(2751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ 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)],[564]) ).
thf(1136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(3956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(1328,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(4350,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).
thf(186,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(1816,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(948,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(3558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(1259,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(4210,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).
thf(137,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(1693,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)],[137]) ).
thf(1169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(4024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(2070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1022,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(3716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(661,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(2961,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(638,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C @ A @ A @ B ) ) @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(2913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C @ A @ A @ B ) ) @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(3323,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Wellfounded_Omlex__prod @ A @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__mlex_0) ).
thf(2714,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Wellfounded_Omlex__prod @ A @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(771,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(3196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(694,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(3030,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1046,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(584,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(2795,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 @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ 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_zero__le__divide__iff_4) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ 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)],[49]) ).
thf(1250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(4193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(2619,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1065,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(3805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(524,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(405,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(2353,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)],[405]) ).
thf(795,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(3244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(663,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ C @ B @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
thf(2966,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ E ) ) @ ( c_Pair @ C @ B @ E @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ B @ C @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclE_0) ).
thf(2847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ B @ C @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1976,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(916,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(3489,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(1273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(4239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).
thf(868,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ D @ C @ B @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_H_0) ).
thf(3392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ D @ C @ B @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1102,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(3886,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(480,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(2539,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)],[480]) ).
thf(1334,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(4363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(2159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(852,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__if_0) ).
thf(3362,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ B ) @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ B @ A @ ( tc_fun @ A @ A ) ) @ D ) @ B @ A @ A ) @ E ) @ F @ B @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(2810,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(555,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(2731,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(692,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(3025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ B ) @ C )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_H_1) ).
thf(1827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ D @ A ) @ B ) @ C )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(505,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(2600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1384,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(851,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( c_Pair @ E @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(3360,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( c_Pair @ E @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(367,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(2265,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)],[367]) ).
thf(1214,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(4118,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1096,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(3869,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(5,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(1357,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)],[5]) ).
thf(802,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(3259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(4066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1141,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(3965,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(1923,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(4206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(2864,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ E ) ) @ D ) @ ( c_Product__Type_OSigma @ B @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaE_0) ).
thf(4071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ B @ C @ D @ A @ E ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ E ) ) @ D ) @ ( c_Product__Type_OSigma @ B @ C @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(733,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__delta_H_1) ).
thf(3113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ A ) @ ( hAPP @ ( c_fequal @ B ) @ C ) @ tc_bool @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ B ) @ D @ B @ A @ ( tc_fun @ A @ A ) ) @ B @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ E )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1902,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1069,axiom,
! [A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id_0) ).
thf(3812,plain,
! [A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(919,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(3494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(63,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 ) )
!= C )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1505,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 ) )
!= C )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(4271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1621,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1200,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).
thf(4088,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(686,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(3013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(4274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(1962,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ C @ D @ A ) @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(3924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ C @ D @ A ) @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(2887,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(678,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(2998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(25,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(1416,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)],[25]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(1812,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1024,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(3721,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(820,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(3296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(392,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(2321,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(786,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(3227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(617,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(2866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ C @ B @ D @ A ) @ A @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(2832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ B ) @ ( hAPP @ ( c_Nat_Osemiring__1__class_Oof__nat @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(2453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(986,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
thf(3637,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(829,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(3316,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(602,axiom,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ v_P____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PW_1) ).
thf(2834,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ v_P____ ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ v_n____ ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_c____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_e____ ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(4189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 @ C @ B @ D @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero__iff_1) ).
thf(2087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Finite__Set_Osetprod @ B @ C @ D @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1 @ C @ B @ D @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1124,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(3933,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(703,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(3047,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(452,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ F @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(2470,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ F @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(1912,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(956,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(3575,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(2177,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1301,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(4298,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).
thf(4491,plain,
$false,
inference(e,[status(thm)],[1718,1411,1469,2778,1559,2412,2544,2331,1818,3172,2199,3021,1586,1501,4201,1369,2889,1823,2295,2306,3053,2341,3008,2131,2072,4062,3666,4022,3434,3167,4183,3477,3698,2463,1899,1840,3581,3863,3830,2787,2595,1982,2427,2480,3449,4015,1956,1950,1549,1686,4166,1750,3072,4226,4339,2808,2495,3912,2282,2114,1533,3382,2363,4043,4037,2512,2976,4376,2117,2940,1596,2622,3858,2908,2062,1443,2776,2659,3509,3285,3377,2527,3040,3153,2953,2590,1569,1939,3959,2671,1544,2676,3498,4215,2380,3794,3120,3049,2686,4026,3616,2476,3253,3313,2042,1354,1497,3017,2195,1705,1426,3217,4234,1671,4090,1655,3004,3332,3135,3649,3365,2918,4220,2184,1999,2316,3446,2448,3338,2434,2712,3414,1761,4294,1640,2580,3895,2360,3276,2575,3370,1746,1835,3629,3545,1914,3502,2985,2020,1366,2516,2405,2869,3634,2046,2763,1782,4371,1441,3308,2010,3947,4124,3730,1921,4198,3898,2082,4030,1724,1475,2067,1967,4322,4156,3880,1482,3597,4386,2957,3425,3116,2339,3342,3061,3653,1511,3776,2682,3089,1992,2703,3820,3891,3248,3204,3263,3221,3976,2916,3938,4348,2698,3131,4224,1871,3574,1907,2501,1860,2217,4130,3542,3410,1577,1455,2897,3744,2126,3803,2466,2745,2571,2691,3099,3517,2857,2169,1704,3470,3951,4265,4383,3602,3231,4008,1847,2829,1892,3463,3374,4358,2049,4179,2767,1479,1609,2373,1572,3919,4317,3084,3312,3902,3657,1931,3734,4141,2024,3835,4302,2388,2007,3524,1664,2090,3163,3453,3569,2335,2017,1489,2237,4329,3966,2027,3199,4173,2105,1450,4258,2996,3295,2782,2893,1632,2259,4001,3527,3473,3983,2880,1682,3438,3525,4050,3621,2925,1978,3290,3093,3923,1960,3771,4162,3851,2058,2861,2190,3712,2483,2424,2772,2137,1351,1433,2804,1600,3588,2508,2964,2367,2437,3537,1928,4055,3068,4230,4033,3189,3739,3505,1886,3808,3036,2530,2002,3756,2242,2799,2103,1405,3606,3906,1521,3492,2718,3406,2205,1696,3184,2884,4082,1564,1863,3229,3011,3301,3567,1438,3265,2164,3186,4076,2641,4059,3550,3418,1604,2922,3151,3097,3450,3503,3459,4323,2910,3995,3318,3767,2232,4100,4312,1730,3679,2673,1387,3261,3827,3972,2249,2541,1676,2147,4252,1666,1487,3814,1519,3867,1580,2277,3742,2969,4344,3752,3989,4128,3239,3233,3884,4284,2150,3816,1619,4160,3664,2396,3514,3682,3778,2015,4044,1883,3282,1920,4053,3198,2826,3578,2872,4187,3144,3926,2741,2228,3799,2653,3958,2445,4280,2758,3980,1602,3618,2628,3810,3750,3349,3556,3718,3877,3600,1457,4327,1624,3535,1787,3763,2492,4104,2547,2344,3647,4080,3931,3033,3408,1740,1910,3595,2769,1402,1804,1375,3381,4048,3963,4012,3968,1360,1936,3467,1592,2300,2498,3909,3615,2157,2840,3482,2100,1851,3122,2946,2990,1794,1953,2895,4248,2709,1970,3386,2631,2724,2537,4095,3746,3237,1755,3941,2638,4109,2268,4219,3176,4263,2460,4333,1461,2419,4191,3194,3723,1889,1567,4291,3141,3952,2877,1964,1942,4276,1659,3000,2323,3179,2561,3210,3714,3728,2868,4389,4315,1424,3441,2312,3010,2455,1414,1842,1791,2172,2108,2038,1446,2551,3671,2978,2472,3935,1419,3242,3611,3126,1668,2851,4120,1984,2813,1874,1429,1715,4152,2272,3703,1825,2968,2285,2450,2932,3486,3787,1530,1539,2836,2845,3059,3354,2153,2355,4244,2505,3390,2566,1799,3692,2052,3109,3074,4069,2140,4086,2756,3201,1759,1393,1627,2370,3215,4361,3147,2203,3279,2883,3856,2748,2402,2440,2793,1515,2662,1732,3807,3824,4148,1857,1814,3225,3563,4195,3592,1712,3306,3999,3321,2645,3422,3841,2617,4004,3675,4308,3660,1764,4380,3042,3491,3985,2602,3696,4365,3158,2121,2235,2936,2729,3707,1727,2391,2904,4354,2556,4116,3358,2253,2275,2033,3257,3607,3079,4256,3888,3839,2734,3111,3274,4269,3686,4017,2524,3396,3319,1916,2791,3609,2981,2514,4032,3900,3458,3404,2695,4041,4144,3372,3741,1833,4341,3070,2727,3636,2859,2938,1784,3255,2789,3519,3472,2489,3086,1752,1652,3736,3081,3758,3945,3272,4122,1701,3590,2716,3604,2827,2134,3599,2959,3213,1503,3023,3773,2326,4112,1897,3416,3304,2573,3170,3532,3118,2220,1707,2293,3051,2891,2308,3077,3651,3330,2738,4149,3208,4236,1635,3002,3340,1997,2753,3436,3783,2055,3700,2706,3091,1464,2474,2510,2079,1806,2906,2065,3101,2521,2721,2119,3352,4337,2679,4228,3631,1408,2478,3251,4369,3155,2229,2084,2214,2383,2415,1894,3038,2422,2774,3287,1524,2097,3270,1589,2284,1933,2955,1492,3106,3468,1542,1722,4139,1771,2943,4213,4073,1801,4154,2802,4176,3500,3138,2378,3066,1690,3182,2197,3160,2182,2812,2111,4064,1909,3192,4296,3583,1556,2974,1820,3456,2180,3219,2824,4203,1877,1471,2605,3027,3133,4009,2314,2129,3668,2625,2780,4028,3165,4208,4181,3034,2410,2923,1838,2785,2593,3006,3298,2874,2928,1381,2329,2842,2578,1688,3480,1396,2365,2765,3917,3687,2288,4304,2207,3539,2075,4232,2350,1594,1699,2212,3627,4373,1643,2369,3674,3953,3241,2797,2244,1435,2633,2022,3310,1477,3325,4196,2303,3512,4282,3908,2693,1973,4158,1562,4084,2005,4331,1948,1809,3427,2665,3293,1905,3921,3455,2899,3849,3444,2239,3031,1583,1662,4136,2614,1467,2994,2318,3395,3206,2503,1684,2124,4319,1990,2684,2333,2256,2564,3278,2597,1958,4336,1551,4168,2582,3571,1748,2298,4035,3507,3842,2192,3754,3833,2518,3872,2850,4045,2942,3737,3376,3640,1598,1611,2375,2060,1743,2012,3904,2732,3462,4200,3129,3949,4287,1780,2821,2407,3058,2386,4314,2092,3818,4020,3554,3344,3655,4351,3769,2468,4164,2656,3019,1499,2569,3246,3642,4346,1987,3940,1452,1637,2688,3334,3791,3063,2920,3202,4222,1869,3475,2429,3823,2337,3801,1980,3774,1830,3828,4132,2701,2486,4241,3847,3623,1679,3412,3174,2044,3095,3853,2247,1766,3388,1797,3961,1372,3366,4150,4111,3684,4057,1849,2838,2558,3970,3124,4133,2992,1536,4246,3356,2279,2357,2145,1485,4106,4093,2949,3943,4267,2030,4342,2807,3914,2584,4257,3398,4217,1617,2760,2818,1553,2078,2347,1517,2209,3797,1421,3478,3433,4289,4278,3452,2458,1918,1649,3565,3401,1459,4325,2310,1844,3188,3548,2611,4185,3625,4078,3725,2743,1448,4102,2187,3346,4006,1390,2305,4170,1575,3056,2226,2643,1866,3929,1734,4310,3465,3613,2988,2167,2174,3484,2554,3383,3336,4126,3748,2971,1854,3368,1646,2443,1674,3789,2855,3709,2853,2290,2251,2532,1508,1629,3104,3991,3561,2608,3235,2431,3662,3780,2934,2262,4261,2394,1861,3978,3694,4293,2399,3149,3529,1607,2902,2095,4098,3761,3844,2648,3585,3430,1777,3267,4299,3677,2162,3993,1513,2036,3645,1994,4306,3552,3420,1614,2930,1774,3705,4114,3892,1546,3987,3837,2951,3521,1527,3690,4367,2142,3379,4039,1348,3860,3785,2155,4378,2534,3291,3997,2983,3865,4254,3733,2587,2815,2736,1757,4357,3496,3015,4146,3328,2201,1363,1657,3347,3177,3875,2417,1789,2040,2668,3045,1346,2549,3145,2636,2751,3956,4350,1816,1495,3558,4210,1693,4024,2070,3716,2961,1710,2913,3323,2714,3196,3030,3765,2223,2795,1473,4193,2619,3805,2651,2353,3244,2966,2847,1976,3489,4239,3392,3886,2539,4363,2159,3362,2810,2731,3974,3025,1827,2600,1384,3360,1378,2265,4118,3869,1357,3259,4066,3965,1923,4206,1925,2864,1880,1431,4071,3113,1902,3812,3494,1505,1399,4271,2270,1621,4088,3013,4274,1962,3924,1945,1737,2887,2998,1416,1769,1812,3721,3296,2321,3227,2866,2832,2453,3637,3316,2834,4189,2087,3933,3047,2470,1912,3575,2177,4298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 15:24:24 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.12 % [INFO] Parsing done (273ms).
% 2.02/1.13 % [INFO] Running in sequential loop mode.
% 2.42/1.32 % [INFO] eprover registered as external prover.
% 2.42/1.32 % [INFO] cvc4 registered as external prover.
% 2.42/1.33 % [INFO] Scanning for conjecture ...
% 3.03/1.50 % [INFO] Found a conjecture and 1344 axioms. Running axiom selection ...
% 4.02/1.74 % [INFO] Axiom selection finished. Selected 1344 axioms (removed 0 axioms).
% 5.28/2.02 % [INFO] Problem is propositional (TPTP CNF).
% 5.28/2.04 % [INFO] Type checking passed.
% 5.50/2.05 % [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 ...
% 19.48/5.36 % External prover 'e' found a proof!
% 19.48/5.36 % [INFO] Killing All external provers ...
% 19.55/5.36 % Time passed: 4831ms (effective reasoning time: 4223ms)
% 19.55/5.36 % 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)>
% 19.55/5.37 % Axioms used in derivation (1344): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_less__iff__diff__less__0_0, cls_finite__UNIV__card__ge__0_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_le__0__eq_1, cls_rtrancl__idemp_0, cls_neg__0__le__iff__le_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_cuts__eq_1, cls_less__divide__eq_3, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_inf__sup__aci_I2_J_0, cls_rtrancl__induct_3, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_sgn__less_0, cls_converse__tranclE_1, cls_add__0__left_0, cls_in__mktop_1, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_subset__insert_1, cls_power__0_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_le__divide__eq_3, cls_Compl__subset__Compl__iff_1, cls_order__le__less__trans_0, cls_equiv__class__eq__iff_0, cls_mult__zero__right_0, cls_sym__conv__converse__eq_1, cls_zero__less__one_0, cls_sup__ge1_0, cls_divide__le__eq_2, cls_compl__sup_0, cls_rtrancl__converseD_0, cls_Un__subset__iff_0, cls_order__less__le__trans_0, cls_divide__less__0__iff_0, cls_comm__semiring__class_Odistrib_0, cls_wf__subset_0, cls_card__empty_0, cls_zero__less__divide__iff_5, cls_of__nat__0_0, cls_insert__inter__insert_0, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_insertE_0, cls_dvd__mult__right_0, cls_setprod__1_H_0, cls_congruent_Ocongruent_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_single__valuedD_0, cls_wf__acyclic_0, cls_sup__top__left_0, cls_le__minus__self__iff_0, cls_sgn__if_2, cls_xt1_I12_J_0, cls_divide__self_0, cls_mult__nonneg__nonpos2_0, cls_rtrancl_Ocases_0, cls_finite__insert_0, cls_sum__squares__eq__zero__iff_0, cls_Image__singleton__iff_0, cls_sgn__times_0, cls_left__minus_0, cls_square__eq__iff_1, cls_Un__empty__left_0, cls_le__funD_0, cls_setprod__Un__Int_0, cls_COMBC__def_0, cls_mult__less__cancel__right__disj_0, cls_subset__empty_1, cls_dvd__setprod_0, cls_divide__nonpos__neg_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_minus__zero_0, cls_tranclD2_0, cls_mult__less__cancel__left__disj_1, cls_sup__bot__right_0, cls_zero__le__one_0, cls_insert__code_1, cls_wfE__min_0, clsarity_nat__Lattices_Odistrib__lattice, cls_power__eq__0__iff_1, cls_single__valued__Id__on_0, cls_termination__basic__simps_I5_J_0, cls_trancl_Ocases_0, cls_add__increasing2_0, cls_setsum__Un_0, cls_less__half__sum_0, clsarity_bool__Lattices_Olower__semilattice, cls_add__sup__distrib__right_0, cls_le__iff__inf_1, cls_Un__upper1_0, cls_of__nat__less__iff_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, cls_Id__O__R_0, cls_divide__1_0, cls_add__strict__right__mono_0, cls_CHAINED_0, cls_power__increasing_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_card__gt__0__iff_1, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, cls_finite__Un_2, cls_irrefl__def_0, cls_acc__wfD_0, cls_diff__add__cancel_0, cls_UnCI_1, cls_zero__le__divide__iff_2, cls_tranclD_0, cls_sgn0_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_add__imp__eq_0, cls_divide__le__0__1__iff_1, cls_le__inf__iff_1, cls_divide__le__eq_7, cls_frac__le_0, cls_add__le__cancel__right_1, cls_minus__le__self__iff_0, cls_wf__inv__image_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_zero__less__divide__iff_0, cls_dvd__diff_0, cls_setsum__Un__disjoint_0, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_Int__insert__left_0, cls_card__eq__0__iff_2, cls_empty__iff_0, cls_class__semiring_Osemiring__rules_I10_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_setsum__Un__Int_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_Domain__iff_0, cls_Domain__rtrancl_0, cls_less__supI1_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_rtrancl__trans_0, cls_mult__nonpos__nonneg_0, cls_mem__def_1, cls_minus__divide__right_0, clsarity_nat__Orderings_Olinorder, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_power__le__imp__le__exp_0, cls_minus__minus_0, cls_card__insert__if_0, cls_le__eq__neg_0, cls_comm__monoid__add_Omult__assoc_0, cls_divide__less__eq_5, cls_antisymD_0, cls_refl__on__converse_0, cls_of__nat__setprod_0, cls_mult__le__cancel__left__pos_0, cls_minus__dvd__iff_1, cls_inf1E_1, cls_divide__eq__eq_0, cls_mult__nonpos__nonpos_0, cls_Image__Un_0, cls_class__ring_Osub__add_0, cls_in__mkbot_4, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_insert__iff_1, cls_add__nonpos__neg_0, cls_wf__union__compatible_0, cls_mult__less__imp__less__right_0, cls_insert__subset_0, cls_refl__Id_0, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_vimage__if_3, cls_class__semiring_Osemiring__rules_I14_J_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_of__nat__0__less__iff_0, cls_add__cancel__21_1, clsarity_fun__Lattices_Oupper__semilattice, cls_le__sup__iff_0, cls_ComplD_0, cls_set__rev__mp_0, cls_inf__left__commute_0, cls_acc_Oinducts_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_wf__induct__rule_0, cls_power__less__imp__less__exp_0, cls_pred__equals__eq_0, cls_minus__unique_0, cls_split__mult__neg__le_0, cls_converse__rtrancl__induct_3, cls_mult__less__imp__less__left_0, cls_sum__squares__le__zero__iff_1, cls_congruent2_Ocongruent2_0, clsarity_fun__Orderings_Otop, cls_setsum__insert_0, cls_rtrancl__into__trancl1_0, cls_divide__strict__left__mono_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_le__0__eq_0, cls_disjoint__eq__subset__Compl_0, cls_divide__le__0__iff_3, cls_gr0I_0, cls_inf__commute_0, cls_DomainE_0, cls_less__divide__eq_4, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_sup__compl__top_0, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_mult__less__cancel__right__disj_3, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, cls_eq__add__iff1_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_mult__eq__0__iff_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_finite__insert_1, cls_add__nonneg__pos_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_wf__converse__trancl_0, cls_diff__eq_0, cls_COMBS__def_0, cls_ab__left__minus_0, cls_Image__iff_0, cls_one__le__power_0, cls_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, cls_sym__Id__on_0, cls_mult__left__mono__neg_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_rtrancl__mono_0, cls_inf__0__imp__0_0, cls_divide__neg__neg_0, cls_antisym__converse_0, cls_nat__less__cases_0, cls_eq__divide__eq_4, cls_mult__mono_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_Un__Int__distrib2_0, cls_finite__Int_1, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_Int__empty__right_0, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, cls_gr__implies__not0_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_rel__compEpair_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_compl__bot__eq_0, cls_setprod__dividef_0, cls_le__antisym_0, cls_add__right__mono_0, cls_le__supI_0, cls_inf__eq__neg__sup_0, cls_Un__subset__iff_1, cls_less__add__iff2_0, cls_of__nat__le__iff_1, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_rtrancl__unfold_0, cls_less__iff__diff__less__0_1, cls_neg__sup__eq__inf_0, cls_power__0__left_0, cls_Image__empty_0, cls_rtrancl__induct_2, cls_of__nat__le__iff_0, cls_Image__iff_1, cls_class__semiring_Omul__c_0, cls_le__supE_1, cls_le__iff__sup_0, cls_setprod__zero__iff_2, cls_wf__insert_0, cls_Domain__Id_0, cls_mult__pos__neg_0, cls_order__eq__refl_0, cls_zero__le__mult__iff_0, cls_setprod__delta_0, cls_mult__strict__mono_0, cls_sgn__pos_0, cls_converse__rtranclE_1, cls_order__le__less_0, cls_order__less__asym_H_0, cls_converse__rtrancl__into__rtrancl_0, cls_double__eq__0__iff_1, cls_wfE__min_1, cls_rtrancl__reflcl_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_mult__strict__right__mono_0, clsarity_fun__Orderings_Obot, cls_card__seteq_0, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_mult__dvd__mono_0, cls_linorder__antisym__conv2_0, cls_wf__induct_1, cls_add__cancel__end_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_sym__trancl_0, cls_sup__eq__neg__inf_0, cls_r__into__trancl_H_0, cls_acc__wfI_0, cls_dvd__mult__cancel__right_2, cls_finite__Int_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_minus__add__cancel_0, cls_le__divide__eq_7, cls_Un__empty__right_0, cls_insert__ident_0, cls_neg__0__le__iff__le_0, cls_tranclE_1, cls_wf__acc__iff_1, cls_minus__less__iff_1, cls_vimageI_0, cls_Image__Id__on_0, cls_Range__converse_0, cls_power__one__over_0, cls_cuts__eq_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_Un__UNIV__right_0, cls_SigmaI_0, cls_linorder__neqE__nat_0, cls_divide__left__mono__neg_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__divide__eq_7, cls_inf__sup__aci_I8_J_0, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_rtrancl__eq__or__trancl_0, cls_wf__induct__rule_1, cls_le__imp__power__dvd_0, cls_xt1_I10_J_0, cls_le__divide__eq_2, cls_refl__on__def_1, cls_add__less__cancel__right_1, cls_not__less__iff__gr__or__eq_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_trancl_Ocases_1, cls_wf__trancl_0, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_le__minus__iff_0, cls_add__left__mono_0, cls_sup__eq__bot__eq2_0, cls_add__nonneg__eq__0__iff_0, cls_RangeE_0, cls_neg__less__eq__nonneg_0, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_Int__insert__right_1, cls_PW_1, cls_add__divide__distrib_0, cls_divide__le__eq_3, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_Compl__disjoint2_0, cls_setprod__1_H_1, cls_no__zero__divisors_0, cls_inf__top__right_0, cls_rtrancl__converse_0, cls_mult__frac__num_0, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, cls_divide__less__eq_0, cls_vimage__if_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_neg__less__eq__nonneg_1, cls_CHAINED_1, cls_mult__frac__frac_0, cls_ATP__Linkup_OCOMBC__def_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_finite_0, cls_add__strict__left__mono_0, cls_single__valued__rel__comp_0, cls_subset__empty_0, cls_in__mkbot_3, cls_subset__Compl__self__eq_1, cls_combine__common__factor_0, cls_converse__Un_0, cls_r__comp__rtrancl__eq_0, cls_singleton__iff_1, cls_class__semiring_Osemiring__rules_I2_J_0, cls_subset__iff_0, cls_card__gt__0__iff_2, cls_setsum__delta_0, cls_insert__code_2, cls_CHAINED_0_01, cls_mult__1__right_0, cls_sgn__greater_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_wf__comp__self_0, clsarity_fun__HOL_Oord, cls_Compl__Un_0, cls_sgn__0__0_0, cls_of__nat__0__le__iff_0, cls_less__divide__eq_2, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_power__strict__increasing_0, cls_rel__comp__distrib_0, cls_equiv__class__eq_0, cls_setsum__eq__0__iff_0, cls_rev__predicate1D_0, cls_le__iff__diff__le__0_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_rtrancl_Ocases_1, cls_mult__neg__pos_0, cls_sgn__neg_0, cls_less__add__iff1_0, cls_inf__eq__top__eq1_0, cls_zero__less__divide__iff_1, cls_mult__right__le__imp__le_0, cls_acc__downwards__aux_0, cls_vimage__Un_0, cls_compl__top__eq_0, cls_inf__absorb2_0, cls_power__eq__0__iff_2, cls_wf__def_1, cls_Range__iff_0, cls_class__ringb_Onoteq__reduce_1, cls_Compl__disjoint_0, cls_acc__induct_2, cls_neg__le__0__iff__le_0, cls_sgn__0__0_1, cls_setsum__delta_H_1, cls_mult__pos__neg2_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_Range__iff_1, cls_diff__minus_0, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_tranclD_1, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_dvd__trans_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, cls_UNIV__not__empty_0, cls_le__minus__iff_1, cls_zero__le__divide__iff_3, cls_Un__insert__left_0, cls_le__eq__neg_1, cls_mlex__less_0, cls_inf__sup__ord_I2_J_0, cls_le__add__iff1_1, cls_inf__period_I4_J_0, cls_doubleton__eq__iff_2, cls_Compl__partition2_0, cls_add__eq__inf__sup_0, cls_vimage__singleton__eq_1, cls_pair__in__Id__conv_0, cls_rtrancl__Un__rtrancl_0, clsarity_nat__Lattices_Olower__semilattice, cls_add__right__cancel_0, cls_less__add__iff2_1, cls_mult__le__cancel__left__neg_1, cls_eq__divide__eq_3, cls_Un__mono_0, cls_divide__self__if_0, cls_insert__subset_1, cls_Int__empty__left_0, cls_setprod__dvd__setprod__subset_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_class__semiring_Osemiring__rules_I19_J_0, clsarity_nat__Orderings_Obot, cls_wf__irrefl_0, cls_Id__on__iff_0, cls_xt1_I8_J_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_diff__def_0, cls_rtrancl__induct_1, cls_eq__divide__eq_0, cls_ex__in__conv_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_IdE_0, cls_dvd__minus__iff_1, cls_mult__le__cancel__left__pos_1, cls_zero__less__mult__pos_0, cls_divide__self__if_1, cls_mult__le__0__iff_1, cls_SigmaD2_0, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_finite__UnI_0, cls_inf__sup__aci_I3_J_0, cls_trancl__reflcl_0, cls_Image__subset__eq_1, cls_set__eq__subset_2, cls_of__nat__eq__iff_0, cls_trancl__domain_0, cls_less__infI1_0, cls_converse__Id__on_0, cls_Compl__UNIV__eq_0, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, cls_Int__insert__left_1, cls_converse__rtranclE_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_class__semiring_Oadd__0_0, cls_Image__singleton__iff_1, clsarity_nat__Nat_Osemiring__char__0, cls_power__less__power__Suc_0, cls_mult__imp__div__pos__le_0, cls_comm__monoid__add_Omult__commute_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_setprod__Un__disjoint_0, cls_power__strict__mono_0, clsarity_prod__Finite__Set_Ofinite_Ofinite, cls_DomainI_0, cls_of__nat__0__less__iff_1, cls_dvd__triv__right_0, cls_class__ringb_Oadd__mul__solve_0, cls_neg__0__less__iff__less_0, cls_neg__less__0__iff__less_0, cls_sum__squares__eq__zero__iff_1, cls_power__strict__decreasing_0, cls_zero__le__divide__iff_5, cls_setsum__addf_0, cls_setprod__infinite_0, cls_mult__le__0__iff_4, cls_Un__empty_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0, cls_linorder__linear_0, cls_Range__rtrancl_0, cls_neg__inf__eq__sup_0, cls_zero__less__two_0, cls_le__minus__self__iff_1, cls_refl__rtrancl_0, cls_rtrancl__reflcl__absorb_0, cls_compl__inf__bot_0, cls_less__add__one_0, cls_not__leE_0, cls_Un__subset__iff_2, cls_ATP__Linkup_OCOMBB__def_0, cls_add__strict__mono_0, cls_nonzero__minus__divide__right_0, clsarity_fun__Lattices_Olattice, clsarity_nat__Ring__and__Field_Omult__mono, cls_wf__asym_0, cls_neg__equal__0__iff__equal_0, cls_divide__less__0__iff_3, cls_zero__less__power_0, cls_setsum__def_1, cls_acc_Oinduct_1, cls_add__cancel__21_0, cls_order__trans_0, cls_dvd__add_0, cls_power__divide_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_inf__le2_0, cls_in__mktop_5, cls_divide__less__eq_8, cls_Int__assoc_0, cls_mult__less__cancel__right__disj_2, cls_setsum__0_H_1, cls_minus__le__self__iff_1, cls_order__antisym_0, cls_setsum__restrict__set_0, cls_divide__le__eq_6, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_eq__add__iff1_1, cls_setprod__pos_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_acc__downwards_0, cls_divide__nonneg__neg_0, cls_sgn__1__neg_0, cls_wf__eq__minimal_1, cls_finite__UNIV_0, cls_Compl__subset__Compl__iff_0, cls_divide__less__eq_1, cls_mult__left__less__imp__less_0, cls_divide__le__0__iff_2, cls_sym__rtrancl_0, cls_ab__diff__minus_0, cls_class__semiring_Omul__d_0, cls_subset__trans_0, cls_neg__equal__zero_1, cls_in__mktop_0, cls_converse__rtrancl__induct_2, cls_refl__onD2_0, cls_Compl__eq__Compl__iff_0, cls_acc_Ocases_0, cls_insert__is__Un_0, cls_linorder__antisym__conv1_1, cls_Domain__Un__eq_0, cls_no__zero__divirors__neq0_0, cls_rtrancl__eq__or__trancl_1, cls_diff__self_0, cls_empty__not__insert_0, cls_card__insert__le_0, cls_zero__neq__one_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_dvd__refl_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_in__mkbot_2, cls_Id__onE_1, cls_insertI1_0, cls_less__divide__eq_5, cls_SigmaD1_0, cls_split__mult__pos__le_1, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_add__frac__eq_0, cls_dvd__mult__cancel__left_2, cls_Image__iff_2, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_le__supE_0, cls_less__divide__eq_8, cls_divide__le__eq_0, cls_subset__Compl__self__eq_0, cls_mult__le__0__iff_5, cls_zero__less__divide__iff_3, cls_inf__compl__bot_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_add__num__frac_0, cls_sup__assoc_0, cls_mult__strict__mono_H_0, cls_Image__Int__subset_0, cls_acc_Oinduct_0, cls_group__add__class_Odiff__0_0, cls_zero__le__divide__iff_4, cls_le__add__iff2_1, cls_dvd__mult__cancel__right_1, cls_neq0__conv_1, cls_less__1__mult_0, cls_in__mktop_4, cls_Un__absorb1_0, cls_sup__top__right_0, cls_wfE__pf_0, cls_subset__refl_0, cls_add__diff__cancel_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_divide__le__0__iff_5, cls_linorder__not__le_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sym__converse_0, cls_sup1E_0, cls_in__inv__image_1, cls_distrib__inf__le_0, cls_Int__commute_0, cls_Un__UNIV__left_0, cls_divide__nonneg__pos_0, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_setprod__delta_1, cls_converse__iff_1, cls_minus__less__iff_0, cls_refl__onD_0, cls_setprod__timesf_0, cls_mult__less__cancel__right__disj_5, cls_sup__least_0, cls_setsum__0_H_0, cls_tranclE_0, cls_le__trans_0, cls_rev__ImageI_0, cls_Pair__eq_0, cls_rtranclE_0, cls_PW_0, cls_singletonE_0, cls_class__semiring_Omul__a_0, cls_Image__mono_0, cls_less__eq__neg__nonpos_1, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_mult__nonneg__nonpos_0, cls_le__inf__iff_2, clsarity_nat__Ring__and__Field_Odvd, cls_Nitpick_Ortrancl__def_0, cls_divide__le__eq_4, clsarity_nat__Orderings_Opreorder, cls_total__on__empty_0, cls_not__less__iff__gr__or__eq_1, cls_setprod__def_1, cls_neg__0__equal__iff__equal_1, cls_le__add__iff1_0, clsarity_nat__Lattices_Olattice, cls_UNIV__I_0, cls_zero__le__square_0, cls_R__O__Id_0, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_equation__minus__iff_0, cls_sup1CI_1, cls_less__minus__iff_1, cls_inf__period_I4_J_1, cls_setprod__empty_0, cls_insertCI_0, cls_order__le__neq__trans_0, cls_le__infE_0, clsarity_fun__Lattices_Oboolean__algebra, cls_card__mono_0, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_pair__in__Id__conv_1, cls_pred__subset__eq_1, cls_tranclD2_1, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_subset__equiv__class_0, cls_vimage__Int_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_ImageE_1, cls_order__eq__iff_2, cls_trancl__unfold__left_0, cls_inf__assoc_0, cls_setsum__delta_H_0, cls_divide__pos__neg_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_le__divide__eq_1, cls_divide__le__0__iff_1, cls_antisym__reflcl_0, cls_setsum__left__distrib_0, cls_less__divide__eq_1, cls_top1I_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_zero__less__divide__iff_2, cls_right__minus__eq_1, cls_less__not__refl_0, cls_le__infI1_0, cls_not__square__less__zero_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_add__inf__distrib__left_0, cls_Int__absorb_0, cls_converse__Id_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_less__add__iff1_1, cls_mult__imp__less__div__pos_0, cls_diff__minus__eq__add_0, cls_rtrancl__trancl__trancl_0, cls_refl__on__Un_0, cls_le__divide__eq_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_Int__lower2_0, cls_le__divide__eq_6, cls_rel__compI_0, cls_insert__mono_0, cls_dvd__triv__left_0, cls_le__supI2_0, cls_class__ringb_Oadd__cancel_0, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_Int__UNIV__right_0, cls_setsum__delta_1, cls_sgn__greater_1, cls_Un__assoc_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_bex__empty_0, cls_mult__eq__0__iff_2, cls_setprod__zero_0, cls_inf__sup__ord_I4_J_0, cls_add__nonneg__nonneg_0, cls_total__on__converse_1, cls_class__ring_Oneg__mul_0, cls_Range__Id_0, cls_mult__strict__left__mono__comm_0, cls_converse__inv__image_0, cls_class__ringb_Oadd__r0__iff_0, cls_ImageE_0, cls_setprod__delta_H_1, cls_inf__eq__top__eq2_0, cls_even__less__0__iff_1, cls_UnE_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_wf__union__merge_0, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_Compl__Int_0, cls_power__eq__imp__eq__base_0, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_mult__mono_H_0, cls_neg__le__0__iff__le_1, cls_add__inf__distrib__right_0, cls_acc__subset_0, cls_converseD_0, cls_acc_OaccI_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0, cls_Un__absorb_0, cls_setprod__zero__iff_1, cls_mult__less__cancel__left__neg_1, cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_order__antisym__conv_0, cls_wf__mlex_0, cls_wf__def_0, cls_dvd__minus__iff_0, cls_equiv_Osym_0, cls_add__strict__increasing_0, cls_dvd__power_1, cls_card__eq__0__iff_0, clsarity_bool__Lattices_Olattice, cls_le__imp__neg__le_0, cls_setsum__cases_0, cls_trancl__range_0, cls_power__mult__distrib_0, cls_eq__eqI_0, cls_setsum__commute_0, cls_divide__less__eq_2, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_power__strict__increasing__iff_1, cls_Domain__Id__on_0, cls_Nitpick_Orefl_H__def_0, cls_Int__lower1_0, cls_minus__divide__divide_0, cls_divide__less__0__1__iff_0, cls_one__dvd_0, cls_converse__rtrancl__induct_1, cls_Int__subset__iff_0, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_power__increasing__iff_1, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, cls_eq__divide__imp_0, cls_class__semiring_Osemiring__rules_I11_J_0, cls_vimage__eq_1, cls_refl__on__converse_1, cls_finite__compl_1, cls_refl__onD1_0, cls_order__less__le_2, cls_divide__strict__right__mono__neg_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_nat__neq__iff_0, cls_mult__less__cancel__left__pos_1, clsarity_bool__Lattices_Obounded__lattice, cls_le0_0, cls_finite__subset_0, cls_converse__rel__comp_0, cls_acyclic__insert_2, cls_power__le__dvd_0, cls_rtrancl__converseI_0, cls_sup__left__idem_0, cls_vimage__if_1, cls_divide__eq__imp_0, cls_Not__Domain__rtrancl_0, cls_minus__divide__left_0, cls_neg__0__less__iff__less_1, cls_vimageE_0, cls_insert__subset_2, cls_setsum__right__distrib_0, cls_inf__bot__left_0, cls_inf1I_0, cls_zero__le__mult__iff_1, cls_le__supI1_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, cls_SigmaE_0, cls_mult__le__cancel__left__neg_0, cls_divide__less__eq_7, cls_subsetD_0, cls_power__commutes_0, cls_symD_0, cls_dvd__mult__cancel__left_1, cls_in__measure_0, cls_minus__mult__left_0, cls_sym__def_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_finite__Un_0, cls_xt1_I11_J_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_zero__le__divide__iff_0, cls_setprod__pos_1, cls_add__neg__neg_0, cls_inf__idem_0, cls_mult__imp__div__pos__less_0, cls_single__valued__confluent_0, cls_equiv__class__subset_0, cls_one__neq__zero_0, cls_double__eq__0__iff_0, clsarity_fun__Lattices_Obounded__lattice, cls_acc_Oinducts_2, cls_mult__le__0__iff_2, cls_divide__less__0__iff_5, cls_dvd__mult__left_0, cls_inf__sup__aci_I4_J_0, cls_add__minus__cancel_0, cls_irrefl__trancl__rD_0, cls_double__compl_0, cls_zero__less__mult__pos2_0, cls_converse__converse_0, cls_insert__absorb2_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_Image__subset__eq_0, cls_mult__right__le__one__le_0, cls_IdI_0, cls_neg__less__0__iff__less_1, cls_comm__monoid__add_Omult__left__commute_0, cls_vimage__singleton__eq_0, cls_add__frac__num_0, cls_mult__right__mono__neg_0, cls_neg__equal__zero_0, cls_sgn__sgn_0, cls_sum__squares__eq__zero__iff_2, cls_diff__divide__distrib_0, cls_sup__inf__absorb_0, cls_irrefl__def_1, cls_divide__less__0__iff_2, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_refl__reflcl_0, cls_setsum__empty_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_acyclic__converse_0, cls_subset__singletonD_0, cls_sup__eq__if_0, cls_wf__induct_0, cls_RangeI_0, cls_Int__iff_2, cls_vimage__code_1, cls_ComplI_0, cls_acc__induct_1, cls_mult__less__cancel__left__disj_3, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_nat__less__le_0, cls_rtrancl__induct_0, cls_divide__left__mono_0, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_eq__equiv__class__iff_0, cls_mult__1_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_setprod__gen__delta_1, cls_mult__1__left_0, cls_nat__le__linear_0, cls_equiv__class__eq__iff_1, cls_zero__less__divide__1__iff_1, cls_in__mkbot_1, cls_comm__monoid__add_Omult__1_0, cls_frac__eq__eq_1, cls_tfl__wf__induct_0, cls_IntI_0, cls_in__inv__image_0, cls_eq__equiv__class_0, cls_ATP__Linkup_OCOMBS__def_0, cls_minus__le__iff_1, cls_mult__less__cancel__right__disj_4, cls_inf__greatest_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_eq__add__iff2_0, cls_zero__le__divide__1__iff_1, cls_cuts__eq_2, cls_mult__zero__left_0, cls_dvd__mult__cancel__right_0, cls_nat__less__le_2, cls_divide__le__0__iff_4, cls_Un__left__absorb_0, cls_linorder__not__le_0, cls_converse__tranclE_0, cls_sgn__less_1, cls_in__mktop_2, cls_less__eq__neg__nonpos_0, cls_le__divide__eq_9, cls_nonzero__power__divide_0, cls_one__less__power_0, cls_dvd__power__le_0, cls_neg__le__iff__le_0, cls_less__minus__self__iff_1, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0, cls_le__iff__inf_0, clsarity_bool__Lattices_Oboolean__algebra, cls_order__less__irrefl_0, cls_rtrancl__eq__or__trancl_2, cls_subset__insert_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_sup__idem_0, cls_frac__less2_0, clsarity_nat__Lattices_Oupper__semilattice, cls_gt__half__sum_0, cls_emptyE_0, cls_antisym__subset_0, cls_acyclic__insert_0, cls_inf__sup__ord_I3_J_0, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_add__nonneg__eq__0__iff_2, cls_less__infI2_0, cls_le__divide__eq_4, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_congruent2__implies__congruent_0, cls_inf__sup__aci_I5_J_0, cls_diff__frac__eq_0, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_dvd__0__right_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_class__semiring_Oadd__c_0, cls_less__divide__eq_6, cls_trancl_Or__into__trancl_0, cls_mult__pos__pos_0, cls_singleton__inject_0, cls_less__eqI_0, cls_neg__0__equal__iff__equal_0, cls_tfl__wf__induct_1, cls_mult__left__le__imp__le_0, cls_less__supI2_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_divide__less__0__iff_1, cls_Un__empty_1, clsarity_fun__Orderings_Opreorder, cls_zero__less__divide__iff_4, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_IntE_1, cls_mult__right__less__imp__less_0, cls_less__minus__self__iff_0, cls_double__complement_0, cls_rtrancl__subset__rtrancl_0, cls_sum__squares__gt__zero__iff_0, cls_trancl__unfold__right_0, cls_dvd__power_0, cls_sgn__1__pos_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_vimageI2_0, cls_sup__ge2_0, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_divide__le__0__iff_0, cls_compl__unique_0, cls_IntE_0, cls_in__mkbot_5, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_equation__minus__iff_1, cls_trancl__rtrancl__trancl_0, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_divide__less__eq_9, cls_add__neg__nonpos_0, cls_add__sup__distrib__left_0, cls_mult__divide__mult__cancel__right_0, cls_card__eq__UNIV__imp__eq__UNIV_0, cls_frac__less_0, cls_mem__Sigma__iff_2, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_insertCI_1, cls_divide__strict__right__mono_0, cls_rtranclD_0, cls_right__minus_0, cls_nonzero__minus__divide__divide_0, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_not__less0_0, cls_le__infE_1, cls_mult__less__cancel__left__disj_2, cls_finite_OemptyI_0, cls_minus__add_0, cls_Int__UNIV__left_0, cls_dvdI_0, cls_pred__subset__eq_0, cls_of__nat__setsum_0, cls_acc__downward_0, cls_acc__induct__rule_1, cls_subset__UNIV_0, cls_trancl__mono_0, cls_acyclic__subset_0, cls_r__into__rtrancl_0, cls_mult__less__cancel__right__disj_1, cls_setsum__negf_0, cls_wf__measure_0, cls_divide__le__eq_9, cls_rtrancl__Un__subset_0, cls_eq__iff__diff__eq__0_1, cls_acc__induct_0, cls_inf__le1_0, cls_rel__comp__mono_0, cls_add__less__cancel__left_0, cls_rtrancl__idemp__self__comp_0, cls_refl__on__comp__subset_0, cls_inf__left__idem_0, cls_class__ringb_Osubr0__iff_1, cls_doubleton__eq__iff_4, cls_minus__dvd__iff_0, cls_divide__less__eq_6, cls_compl__inf_0, cls_acc_OaccI_1, cls_insert__code_0, cls_subset__insertI_0, cls_acc_Oinducts_1, cls_Domain__mono_0, cls_total__on__converse_0, cls_trancl__trans_0, cls_converse__rtrancl__induct_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_single__valued__subset_0, cls_sup__eq__if_1, cls_le__eqI_1, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_vimageD_0, cls_add__less__le__mono_0, cls_divide__nonpos__pos_0, cls_card__gt__0__iff_0, cls_trancl__unfold_0, cls_zero__le__power_0, cls_power__increasing__iff_0, cls_divide__less__eq_3, cls_sgn__if_1, clsarity_nat__Ring__and__Field_Osemiring__1, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_antisym__def_0, cls_less__divide__eq_0, cls_order__less__imp__le_0, cls_Image__Int__eq_0, cls_minus__equation__iff_1, cls_Un__Image_0, cls_equiv__class__nondisjoint_0, cls_eq__neg__iff__add__eq__0_0, cls_finite__Un_1, cls_disjoint__iff__not__equal_0, cls_Not__Domain__rtrancl_1, cls_add__strict__increasing2_0, cls_class__ringb_Osubr0__iff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_equiv__comp__eq_0, cls_monoid__add__class_Oadd__0__right_0, cls_setprod__insert_0, cls_of__nat__less__iff_1, cls_mult__idem_0, cls_le__infI2_0, cls_dvd__mult_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_setsum__divide__distrib_0, cls_rev__finite__subset_0, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_Nitpick_Orefl_H__def_1, cls_inf__top__left_0, cls_le__eq__less__or__eq_0, cls_setsum__subtractf_0, cls_vimage__empty_0, cls_Un__Int__assoc__eq_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_compl__sup__top_0, cls_eq__iff__diff__eq__0_0, cls_setsum__infinite_0, cls_mlex__leq_0, cls_insert__commute_0, cls_complete__Lin_1, cls_insert__iff_2, cls_xt1_I7_J_0, cls_setprod__delta_H_0, cls_acyclic__impl__antisym__rtrancl_0, cls_trancl__converse_0, cls_disjoint__eq__subset__Compl_1, cls_O__assoc_0, cls_acyclic__converse_1, cls_less__eqI_1, cls_vimage__if_2, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, cls_rtranclE_1, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_mult__neg__neg_0, cls_equiv__class__eq__iff_2, cls_linorder__not__less_1, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_not__one__le__zero_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_Un__insert__right_0, cls_mult__less__le__imp__less_0, cls_antisym__converse_1, cls_Pair__eq_1, cls_mult__divide__mult__cancel__left_0, cls_equalityE_0, cls_mult__le__less__imp__less_0, cls_inf__sup__distrib2_0, cls_finite__compl_0, cls_divide__less__0__1__iff_1, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, cls_Compl__empty__eq_0, cls_power__Suc__less_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_wf__Un_0, cls_power__decreasing_0, cls_zero__le__imp__of__nat_0, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_rel__compEpair_1, cls_power__0__left_1, cls_Int__insert__right_0, cls_sup__0__imp__0_0, cls_add__le__cancel__right_0, cls_eq__equiv__class__iff_1, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_right__inverse__eq_1, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_power__mono_0, cls_divide__le__0__1__iff_0, cls_subset__insert__iff_1, cls_le__refl_0, cls_not__acc__down_0, cls_neg__less__iff__less_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_even__less__0__iff_0, clsarity_bool__Orderings_Otop, cls_in__measure_1, cls_in__mkbot_0, cls_ball__empty_0, cls_setprod__zero__iff_0, cls_sum__squares__le__zero__iff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, cls_setprod__pos__nat__iff_0, cls_predicate1D_0, cls_inf1E_0, cls_zero__le__mult__iff_2, cls_dvd__0__left_0, cls_divide__le__eq_1, cls_of__nat__less__0__iff_0
% 19.55/5.37 % No. of inferences in proof: 2691
% 19.55/5.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4831 ms resp. 4223 ms w/o parsing
% 21.02/5.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.02/5.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------