TSTP Solution File: LCL823-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL823-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:32:05 EDT 2023
% Result : Unsatisfiable 17.02s 5.13s
% Output : Refutation 17.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 948
% Syntax : Number of formulae : 1747 ( 547 unt; 150 typ; 0 def)
% Number of atoms : 3327 (1202 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 50420 (1616 ~;1730 |; 0 &;47074 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 152 ( 150 usr; 37 con; 0-9 aty)
% Number of variables : 5898 ( 0 ^;5898 !; 0 ?;5898 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(c_and_type,type,
c_and: $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
thf(c_All_type,type,
c_All: $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_implies_type,type,
c_implies: $i ).
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i ).
thf(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i ).
thf(v_T_____type,type,
v_T____: $i ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i ).
thf(c_Ex_type,type,
c_Ex: $i > $i ).
thf(v_e_____type,type,
v_e____: $i ).
thf(v_i_____type,type,
v_i____: $i ).
thf(v_rs_____type,type,
v_rs____: $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_List_Ofilter_type,type,
c_List_Ofilter: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i > $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tc_Predicate_Opred_type,type,
tc_Predicate_Opred: $i > $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_List_Oset_type,type,
c_List_Oset: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Predicate_Opred_OPred_type,type,
c_Predicate_Opred_OPred: $i > $i > $i ).
thf(c_Transitive__Closure_Ortranclp_type,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(c_Orderings_Oorder__class_Omono_type,type,
c_Orderings_Oorder__class_Omono: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_in_type,type,
c_in: $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_split_type,type,
c_split: $i > $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(c_The_type,type,
c_The: $i > $i > $i ).
thf(c_Lattices_Oboolean__algebra_type,type,
c_Lattices_Oboolean__algebra: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i ).
thf(c_Collect_type,type,
c_Collect: $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_or_type,type,
c_or: $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(c_Orderings_Oorder__class_Ostrict__mono_type,type,
c_Orderings_Oorder__class_Ostrict__mono: $i > $i > $i > $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i > $i ).
thf(v_B_type,type,
v_B: $i ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
thf(c_Predicate_Obind_type,type,
c_Predicate_Obind: $i > $i > $i > $i > $i ).
thf(v_P_type,type,
v_P: $i ).
thf(v_f_type,type,
v_f: $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_Predicate_Oeval_type,type,
c_Predicate_Oeval: $i > $i ).
thf(c_Orderings_Oorder_type,type,
c_Orderings_Oorder: $i > $i > $i > $o ).
thf(c_List_Osko__List__Xin__listsp__conv__set__1__1_type,type,
c_List_Osko__List__Xin__listsp__conv__set__1__1: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Finite__Set_Olattice_OInf__fin_type,type,
c_Finite__Set_Olattice_OInf__fin: $i > $i > $i > $i ).
thf(c_Lattices_Odistrib__lattice_type,type,
c_Lattices_Odistrib__lattice: $i > $i > $i > $i > $i > $o ).
thf(c_Not_type,type,
c_Not: $i ).
thf(v_u_____type,type,
v_u____: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(c_Hilbert__Choice_OLeastM_type,type,
c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Olattice__class_OSup__fin_type,type,
c_Finite__Set_Olattice__class_OSup__fin: $i > $i > $i ).
thf(c_Finite__Set_Olattice_OSup__fin_type,type,
c_Finite__Set_Olattice_OSup__fin: $i > $i > $i > $i ).
thf(c_Record_Oiso__tuple__update__accessor__cong__assist_type,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i > $i ).
thf(c_Finite__Set_Olattice__class_OInf__fin_type,type,
c_Finite__Set_Olattice__class_OInf__fin: $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i ).
thf(v_ea_______type,type,
v_ea______: $i ).
thf(v_ua_______type,type,
v_ua______: $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $i ).
thf(v_upd_type,type,
v_upd: $i ).
thf(v_acc_type,type,
v_acc: $i ).
thf(c_Finite__Set_Olinorder_OMin_type,type,
c_Finite__Set_Olinorder_OMin: $i > $i > $i > $i ).
thf(c_OrderedGroup_Oordered__ab__semigroup__add_type,type,
c_OrderedGroup_Oordered__ab__semigroup__add: $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Finite__Set_Olinorder_OMax_type,type,
c_Finite__Set_Olinorder_OMax: $i > $i > $i > $i ).
thf(c_Orderings_Oorder_Omono_type,type,
c_Orderings_Oorder_Omono: $i > $i > $i > $i ).
thf(c_FunDef_OTHE__default_type,type,
c_FunDef_OTHE__default: $i > $i > $i > $i ).
thf(v_d_type,type,
v_d: $i ).
thf(c_HOL_OIf_type,type,
c_HOL_OIf: $i > $i > $i > $i > $i ).
thf(c_Orderings_Oorder_Ostrict__mono_type,type,
c_Orderings_Oorder_Ostrict__mono: $i > $i > $i > $i ).
thf(c_Orderings_Oord_OLeast_type,type,
c_Orderings_Oord_OLeast: $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(v_s_type,type,
v_s: $i ).
thf(class_Orderings_Owellorder_type,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(c_Recdef_Oadm__wf_type,type,
c_Recdef_Oadm__wf: $i > $i > $i > $i > $o ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $i ).
thf(c_Predicate_Osingleton_type,type,
c_Predicate_Osingleton: $i > $i > $i > $i ).
thf(v_dfault_type,type,
v_dfault: $i ).
thf(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
thf(c_Type_Otypings_type,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(v_n_____type,type,
v_n____: $i ).
thf(v_T_H_____type,type,
v_T_H____: $i ).
thf(t_c_type,type,
t_c: $i ).
thf(c_Hilbert__Choice_OGreatestM_type,type,
c_Hilbert__Choice_OGreatestM: $i > $i > $i > $i > $i ).
thf(c_List_Osko__List__Xfoldl__apply__inv__1__1_type,type,
c_List_Osko__List__Xfoldl__apply__inv__1__1: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(2094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__def_0) ).
thf(2306,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(365,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
thf(1633,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(523,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Fun_Oid @ B ) ) @ C )
= C )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__def_1) ).
thf(1995,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Fun_Oid @ B ) ) @ C )
= C )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(406,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
thf(1729,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(102,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ) @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib2_0) ).
thf(1031,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(483,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1899,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(45,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(893,plain,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(764,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(2559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(667,axiom,
! [G: $i,F: $i,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ A ) @ ( c_Fun_Oid @ A ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ B @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ B ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ ( tc_fun @ E @ A ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ E @ A ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ E ) ) @ ( c_fequal @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ B ) @ ( c_COMBB @ tc_bool @ tc_bool @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ G ) ) ) ) ) ) ) )
| ~ ( c_Fun_Oinj__on @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) @ B @ E @ A ) @ ( c_Product__Type_OSigma @ D @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_bool ) @ B ) @ G ) @ B @ E ) @ ( tc_prod @ B @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__mult__setsum__if__inj_0) ).
thf(2331,plain,
! [G: $i,F: $i,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ A ) @ ( c_Fun_Oid @ A ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ B @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ B ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ ( tc_fun @ E @ A ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ B @ ( tc_fun @ E @ A ) ) @ ( tc_fun @ B @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ E ) ) @ ( c_fequal @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ B ) @ ( c_COMBB @ tc_bool @ tc_bool @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ G ) ) ) ) ) ) ) )
| ~ ( c_Fun_Oinj__on @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) @ B @ E @ A ) @ ( c_Product__Type_OSigma @ D @ ( hAPP @ ( c_COMBK @ ( tc_fun @ E @ tc_bool ) @ B ) @ G ) @ B @ E ) @ ( tc_prod @ B @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1956,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(611,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(2199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(1586,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1501,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)],[307]) ).
thf(719,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty_0) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oset @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ ( c_List_Oset @ C @ B ) ) @ D )
= ( c_List_Ofoldl @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) ) @ D ) ) @ ( c_Orderings_Otop__class_Otop @ A ) @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INFI__set__fold_0) ).
thf(2109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ ( c_List_Oset @ C @ B ) ) @ D )
= ( c_List_Ofoldl @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) ) @ D ) ) @ ( c_Orderings_Otop__class_Otop @ A ) @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(288,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1454,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(2031,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(333,axiom,
( ( hAPP @ ( c_Relation_OImage @ v_r @ t_a @ t_b ) @ v_s )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_s ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_b ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) ) @ v_r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__def__raw_0) ).
thf(1559,plain,
( ( hAPP @ ( c_Relation_OImage @ v_r @ t_a @ t_b ) @ v_s )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_s ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_b ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) ) @ v_r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I6_J_0) ).
thf(1105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OInf__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Inf1__distrib_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OInf__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(20,axiom,
! [A: $i] : ( class_Lattices_Odistrib__lattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Lattices_Odistrib__lattice) ).
thf(846,plain,
! [A: $i] : ( class_Lattices_Odistrib__lattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(228,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_0) ).
thf(1315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_The @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ C ) ) ) ) @ ( hAPP @ ( c_fequal @ B ) @ D ) ) @ A @ B @ tc_bool ) @ ( tc_prod @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_The__split__eq_0) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_The @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ C ) ) ) ) @ ( hAPP @ ( c_fequal @ B ) @ D ) ) @ A @ B @ tc_bool ) @ ( tc_prod @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(962,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)],[74]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ B @ D @ E ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(1818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ B @ D @ E ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(219,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ C @ A @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Osup__inf__distrib1_0) ).
thf(1295,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ C @ A @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(160,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ B @ E @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__inf_0) ).
thf(1158,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ B @ E @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(2117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(2231,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(2395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1618,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ C ) ) ) @ D ) @ A @ B @ tc_bool ) )
= ( c_Product__Type_OSigma @ ( hAPP @ ( c_Collect @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( c_Collect @ B ) ) @ D ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetCompr__Sigma__eq_0) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ C ) ) ) @ D ) @ A @ B @ tc_bool ) )
= ( c_Product__Type_OSigma @ ( hAPP @ ( c_Collect @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( c_Collect @ B ) ) @ D ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBS @ B @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ A ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ A ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ B ) ) @ ( c_fequal @ A ) ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__image__set_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBS @ B @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ A ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ A ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ B ) ) @ ( c_fequal @ A ) ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1205,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)],[179]) ).
thf(573,axiom,
! [B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_List_Oset @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty2_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_List_Oset @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(688,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(2380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1793,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(389,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1692,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(223,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ C @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ F ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(1305,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ C @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ F ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_1) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__less_0) ).
thf(1924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(616,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_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(2210,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_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1808,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)],[442]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ B ) ) @ A ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__filter_0) ).
thf(1569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Ofilter @ B @ C @ D ) @ D )
= ( c_List_Ofilter @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ B ) ) @ A ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( c_Predicate_Opred_OPred @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval_Osimps_0) ).
thf(1939,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( c_Predicate_Opred_OPred @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(395,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(785,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I5_J_0) ).
thf(2607,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_List_Onth @ B @ A ) @ C ) ) @ ( c_List_Oset @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__mem_0) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_List_Onth @ B @ A ) @ C ) ) @ ( c_List_Oset @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(605,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(2184,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(2448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(2141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1872,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)],[472]) ).
thf(520,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(1988,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(53,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(913,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(67,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
thf(945,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(506,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_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1954,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_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1788,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)],[433]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1426,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)],[276]) ).
thf(729,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(2476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ D ) @ B ) @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(597,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(2168,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_prod @ B @ A ) ) @ ( tc_fun @ A @ C ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ A ) @ C @ A ) @ D ) ) @ ( c_Pair @ B @ A ) ) @ B @ A @ C )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__eta_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_prod @ B @ A ) ) @ ( tc_fun @ A @ C ) @ B ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ A ) @ C @ A ) @ D ) ) @ ( c_Pair @ B @ A ) ) @ B @ A @ C )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(2580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1354,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(587,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(2146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(930,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(679,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(2360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__less_1) ).
thf(1095,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(546,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(2046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(759,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(2548,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(282,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Int__distrib_0) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1613,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(529,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_1) ).
thf(2010,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(248,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1359,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(561,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ A @ H @ D @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__inf__bot_0) ).
thf(2082,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ A @ H @ D @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(747,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ E ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ C @ E @ F @ G @ H @ I @ J @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__Sup_0) ).
thf(2516,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ E ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ C @ E @ F @ G @ H @ I @ J @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( ( hAPP @ C @ D )
!= ( hAPP @ C @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__eq_0) ).
thf(1529,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( ( hAPP @ C @ D )
!= ( hAPP @ C @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(699,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_0) ).
thf(2405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(478,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( c_Predicate_Obind @ B @ C @ D @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( hAPP @ C @ F ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ D ) @ B ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bindI_0) ).
thf(1887,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( c_Predicate_Obind @ B @ C @ D @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ ( hAPP @ C @ F ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oeval @ D ) @ B ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(624,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ ( c_List_Osko__List__Xfoldl__apply__inv__1__1 @ A @ B @ C @ D ) ) )
!= ( c_List_Osko__List__Xfoldl__apply__inv__1__1 @ A @ B @ C @ D ) )
| ( ( c_List_Ofoldl @ E @ ( hAPP @ A @ F ) @ G @ D @ H )
= ( hAPP @ A @ ( c_List_Ofoldl @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ D ) @ ( tc_fun @ H @ C ) @ C ) @ ( hAPP @ ( c_COMBB @ D @ C @ H ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ H @ D ) @ C ) @ E ) @ A ) ) @ F @ G @ C @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__apply__inv_0) ).
thf(2227,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ ( c_List_Osko__List__Xfoldl__apply__inv__1__1 @ A @ B @ C @ D ) ) )
!= ( c_List_Osko__List__Xfoldl__apply__inv__1__1 @ A @ B @ C @ D ) )
| ( ( c_List_Ofoldl @ E @ ( hAPP @ A @ F ) @ G @ D @ H )
= ( hAPP @ A @ ( c_List_Ofoldl @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ H @ D ) @ ( tc_fun @ H @ C ) @ C ) @ ( hAPP @ ( c_COMBB @ D @ C @ H ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ H @ D ) @ C ) @ E ) @ A ) ) @ F @ G @ C @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(79,axiom,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty2_1) ).
thf(973,plain,
! [A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(41,axiom,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(885,plain,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(372,axiom,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1650,plain,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1645,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)],[370]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(2173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1366,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(486,axiom,
! [G: $i,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 @ ( hAPP @ ( c_COMBS @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ E ) ) ) ) @ F ) ) ) ) @ G )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ G ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ tc_bool ) @ F ) ) ) ) ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ G @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__setsum__restrict_0) ).
thf(1904,plain,
! [G: $i,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 @ ( hAPP @ ( c_COMBS @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ E ) ) ) ) @ F ) ) ) ) @ G )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ G ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ tc_bool ) @ F ) ) ) ) ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ G @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(1518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(200,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1254,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(666,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(2328,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(278,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_1) ).
thf(1430,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(542,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_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(2039,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_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(838,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(452,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ H @ A @ I @ D @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__sup__top_0) ).
thf(1826,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ H @ A @ I @ D @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(765,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ C @ B @ D ) @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(2562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ C @ B @ D ) @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(522,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1992,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)],[522]) ).
thf(579,axiom,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INFI__def__raw_0) ).
thf(2126,plain,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(115,axiom,
( ( c_Predicate_Obind @ v_P @ v_f @ t_a @ t_b )
= ( c_Predicate_Opred_OPred @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_P ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_b @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Predicate_Opred @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_Predicate_Oeval @ t_b ) ) @ v_f ) ) ) ) @ t_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Predicate_Obind__def__raw_0) ).
thf(1059,plain,
( ( c_Predicate_Obind @ v_P @ v_f @ t_a @ t_b )
= ( c_Predicate_Opred_OPred @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_P ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_b @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Predicate_Opred @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_Predicate_Oeval @ t_b ) ) @ v_f ) ) ) ) @ t_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(769,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoD_0) ).
thf(2571,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1760,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_2) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Oorder_Ostrict__mono @ B @ C @ A )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ A ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ C ) @ ( c_All @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBS @ C @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( c_COMBC @ C @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBB @ A @ tc_bool @ C ) ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( c_HOL_Oord__class_Oless @ A ) ) ) ) ) @ ( c_COMBI @ ( tc_fun @ C @ A ) ) ) ) ) ) )
| ~ ( c_Orderings_Oorder @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ostrict__mono__def__raw_0) ).
thf(1907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Oorder_Ostrict__mono @ B @ C @ A )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ A ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ C ) @ ( c_All @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBS @ C @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( c_COMBC @ C @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBB @ A @ tc_bool @ C ) ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( c_HOL_Oord__class_Oless @ A ) ) ) ) ) @ ( c_COMBI @ ( tc_fun @ C @ A ) ) ) ) ) ) )
| ~ ( c_Orderings_Oorder @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(2501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(619,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 @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__iff_0) ).
thf(2217,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 @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(311,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(1511,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(2274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ C ) @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(917,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(454,axiom,
( ( c_Relation_Ototal__on @ v_A @ v_r @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ t_a ) @ c_Not ) ) @ ( c_fequal @ t_a ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_or ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) ) @ v_r ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def__raw_0) ).
thf(1832,plain,
( ( c_Relation_Ototal__on @ v_A @ v_r @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ t_a ) @ c_Not ) ) @ ( c_fequal @ t_a ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_or ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) ) @ v_r ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(934,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(327,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
thf(1545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(853,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exE__some_0) ).
thf(2158,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(534,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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(2024,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)],[534]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2388,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)],[692]) ).
thf(134,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_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1100,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_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1922,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Collect_0) ).
thf(1087,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__map__eq__map_0) ).
thf(1514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(761,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ C @ B @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__top__eq_0) ).
thf(2552,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ C @ B @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_split @ A @ B @ C @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitI_0) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_split @ A @ B @ C @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(141,axiom,
( ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( c_fequal @ t_b ) ) ) @ v_f ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__def__raw_0) ).
thf(1115,plain,
( ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( c_fequal @ t_b ) ) ) @ v_f ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(796,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eq__UN_0) ).
thf(2635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(2301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(445,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1815,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1494,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)],[304]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1450,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)],[286]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1109,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)],[139]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(718,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(2451,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_List_Oset @ A @ B )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ B ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_nat @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ B ) @ ( c_COMBB @ B @ tc_bool @ tc_nat ) ) @ ( c_fequal @ B ) ) ) @ ( c_List_Onth @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_nat @ tc_nat @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__conv__nth_0) ).
thf(1334,plain,
! [B: $i,A: $i] :
( ( c_List_Oset @ A @ B )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ B ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ tc_nat @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ B ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ B ) @ ( c_COMBB @ B @ tc_bool @ tc_nat ) ) @ ( c_fequal @ B ) ) ) @ ( c_List_Onth @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_nat @ tc_nat @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(302,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ B @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Ostrict__mono @ E @ F @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ G @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ostrict__monoD_0) ).
thf(1489,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ B @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Ostrict__mono @ E @ F @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ G @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(789,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(2616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( ( c_Hilbert__Choice_OEps @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEps__psimp_0) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( ( c_Hilbert__Choice_OEps @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conj__eq_0) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(536,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(2027,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(1682,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(468,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1864,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(576,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(2122,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(650,axiom,
! [B: $i,A: $i] :
( ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ A ) ) @ B ) @ v_x @ t_a )
= ( hAPP @ ( hAPP @ c_and @ ( c_List_Olistsp @ A @ v_x @ t_a ) ) @ ( c_List_Olistsp @ B @ v_x @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__conj__eq_0) ).
thf(2291,plain,
! [B: $i,A: $i] :
( ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ A ) ) @ B ) @ v_x @ t_a )
= ( hAPP @ ( hAPP @ c_and @ ( c_List_Olistsp @ A @ v_x @ t_a ) ) @ ( c_List_Olistsp @ B @ v_x @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_0) ).
thf(1020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(2254,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( hAPP @ ( c_Collect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ ( c_List_Oset @ B @ C ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__filter_0) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Ofilter @ A @ B @ C ) @ C )
= ( hAPP @ ( c_Collect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ ( c_List_Oset @ B @ C ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(1051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( c_fequal @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( c_fequal @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(164,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1169,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1377,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(733,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(2483,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(31,axiom,
! [A: $i] : ( class_Orderings_Opreorder @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Orderings_Opreorder) ).
thf(866,plain,
! [A: $i] : ( class_Orderings_Opreorder @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(2371,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(262,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1394,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fin__Inf_0) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(790,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(2618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(646,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(2281,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OGreatestM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ D @ A @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GreatestM__def_0) ).
thf(1896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OGreatestM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ D @ A @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1526,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)],[318]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) ) @ ( c_in @ B ) ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__def_0) ).
thf(2137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) ) @ ( c_in @ B ) ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ E @ B @ C @ D ) )
| ( ( hAPP @ A @ F )
= ( hAPP @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).
thf(988,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ E @ B @ C @ D ) )
| ( ( hAPP @ A @ F )
= ( hAPP @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(648,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ B @ A @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Osup__inf__distrib2_0) ).
thf(2286,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ B @ A @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(798,axiom,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(2639,plain,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_0) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(136,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_e____ ) @ v_u____ ) @ v_T____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(1104,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_e____ ) @ v_u____ ) @ v_T____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I1_J_0) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Omap @ B @ ( c_List_Olist_ONil @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(694,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ A @ B ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(2392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ A @ B ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(590,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ E ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(2154,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ E ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(776,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(2586,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( 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)],[776]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1651,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(613,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2204,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(2473,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1438,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)],[281]) ).
thf(294,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ B @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Oinf__sup__distrib2_0) ).
thf(1470,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ B @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1783,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(652,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/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(2296,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)],[652]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(2364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(595,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ E @ A ) @ D ) @ B ) ) @ ( c_Product__Type_OSigma @ F @ C @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(2164,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ E @ A ) @ D ) @ B ) ) @ ( c_Product__Type_OSigma @ F @ C @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_Orderings_Oorder @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__order_0) ).
thf(1067,plain,
! [A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_Orderings_Oorder @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(409,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oantisym__conv_0) ).
thf(1736,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_0) ).
thf(2496,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1768,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(470,axiom,
( ( c_Relation_Orel__comp @ v_r @ v_s @ t_a @ t_b @ t_c )
= ( hAPP @ ( c_Collect @ ( tc_prod @ t_a @ t_c ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_c ) @ ( c_Ex @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) ) @ t_a ) @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) @ t_c ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_c @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_c ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_b @ t_c ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ t_c ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_b @ t_c ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_b @ t_c ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_b @ t_c @ ( tc_prod @ t_b @ t_c ) ) @ ( c_Pair @ t_b @ t_c ) ) ) ) ) @ v_s ) ) ) @ t_a @ t_c @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__def__raw_0) ).
thf(1868,plain,
( ( c_Relation_Orel__comp @ v_r @ v_s @ t_a @ t_b @ t_c )
= ( hAPP @ ( c_Collect @ ( tc_prod @ t_a @ t_c ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_c ) @ ( c_Ex @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_c @ ( tc_fun @ t_b @ tc_bool ) ) ) @ t_a ) @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) @ t_c ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_c @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_c ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_b @ t_c ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) ) @ t_c ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_b @ t_c ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_b @ t_c ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_b @ t_c ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_b @ t_c @ ( tc_prod @ t_b @ t_c ) ) @ ( c_Pair @ t_b @ t_c ) ) ) ) ) @ v_s ) ) ) @ t_a @ t_c @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(689,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(2382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(552,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ F ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(2061,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ F ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(366,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2E_1) ).
thf(1636,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OSup__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Sup2__distrib_0) ).
thf(1163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OSup__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Obind @ A @ B @ C @ D )
= ( c_Predicate_Opred_OPred @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ C ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Predicate_Opred @ D ) @ ( tc_fun @ D @ tc_bool ) @ C ) @ ( c_Predicate_Oeval @ D ) ) @ B ) ) ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bind__def_0) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Obind @ A @ B @ C @ D )
= ( c_Predicate_Opred_OPred @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ C ) @ A ) ) ) ) @ ( hAPP @ ( c_COMBC @ C @ D @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_Predicate_Opred @ D ) @ ( tc_fun @ D @ tc_bool ) @ C ) @ ( c_Predicate_Oeval @ D ) ) @ B ) ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(2428,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
thf(825,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)],[11]) ).
thf(633,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(2249,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(2541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(29,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(862,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(382,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olattice_OInf__fin @ C @ D @ E ) )
= ( c_Finite__Set_Olattice_OInf__fin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ C @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Osup__Inf1__distrib_0) ).
thf(1676,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olattice_OInf__fin @ C @ D @ E ) )
= ( c_Finite__Set_Olattice_OInf__fin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ C @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
thf(1217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(416,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1751,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(451,axiom,
( ( c_Predicate_OPowp @ v_A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ v_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Powp__def__raw_0) ).
thf(1824,plain,
( ( c_Predicate_OPowp @ v_A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ v_A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(815,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Olist_ONil @ B ) @ B @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(751,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(2528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) ) @ ( c_fequal @ A ) ) ) @ A )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__r__diff__Id_0) ).
thf(2264,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) ) @ ( c_fequal @ A ) ) ) @ A )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(701,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I6_J_0) ).
thf(2409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1387,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)],[259]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(716,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ B @ C ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ D @ B @ E @ F ) )
| ( ( hAPP @ ( hAPP @ D @ A ) @ C )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_update__accessor__noopE_0) ).
thf(2445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ B @ C ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ D @ B @ E @ F ) )
| ( ( hAPP @ ( hAPP @ D @ A ) @ C )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(847,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(492,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ E @ D ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__less__eq_0) ).
thf(1920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ E @ D ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(2433,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ A @ C ) ) @ ( c_List_Oset @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__append_0) ).
thf(1968,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ A @ C ) ) @ ( c_List_Oset @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(331,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_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1555,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_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(168,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(1178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(505,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ C ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ C ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(1951,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ C ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ C ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(387,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__injective_0) ).
thf(1687,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(361,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
thf(1624,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( hAPP @ ( hAPP @ ( c_Pair @ B @ C ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ C ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bounded__ex_2) ).
thf(1836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ C ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(269,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1407,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(261,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_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1392,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_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(488,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Olattice_OSup__fin @ A @ B @ C )
= ( hAPP @ D @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ E @ D @ F @ G @ H @ A @ I @ J @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__fin__Sup_0) ).
thf(1910,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Olattice_OSup__fin @ A @ B @ C )
= ( hAPP @ D @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ E @ D @ F @ G @ H @ A @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_2) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(786,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
thf(2609,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(672,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(2344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2313,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)],[659]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OLeastM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ A @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LeastM__def_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OLeastM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ A @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(737,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2492,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)],[737]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(499,axiom,
! [G: $i,F: $i,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) @ G ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__product_0) ).
thf(1936,plain,
! [G: $i,F: $i,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) @ G ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(518,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 @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(1983,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 @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(421,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__iff_0) ).
thf(1762,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(208,axiom,
! [K: $i,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 @ D @ B ) @ ( hAPP @ E @ C ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ A @ E @ F @ G @ D @ H @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odiff__eq_0) ).
thf(1270,plain,
! [K: $i,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 @ D @ B ) @ ( hAPP @ E @ C ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ A @ E @ F @ G @ D @ H @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(440,axiom,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1804,plain,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(234,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(1328,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(117,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(1064,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(512,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Omap @ C @ D @ E @ F ) @ G @ F )
= ( c_List_Ofoldl @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ E @ F ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ G ) @ ( tc_fun @ ( tc_fun @ E @ F ) @ ( tc_fun @ E @ G ) ) @ G ) @ ( c_COMBB @ F @ G @ E ) ) @ A ) ) @ C ) @ B @ D @ G @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__map_0) ).
thf(1970,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Omap @ C @ D @ E @ F ) @ G @ F )
= ( c_List_Ofoldl @ ( hAPP @ ( hAPP @ ( c_COMBC @ G @ ( tc_fun @ E @ F ) @ ( tc_fun @ E @ G ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ F @ G ) @ ( tc_fun @ ( tc_fun @ E @ F ) @ ( tc_fun @ E @ G ) ) @ G ) @ ( c_COMBB @ F @ G @ E ) ) @ A ) ) @ C ) @ B @ D @ G @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_List_Oset @ D @ C ) ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_List_Oset @ D @ C ) ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(324,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(1540,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ua______ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(475,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert__distrib_0) ).
thf(1878,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(869,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)],[34]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ~ ( hBOOL @ ( hAPP @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__Least_0) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ~ ( hBOOL @ ( hAPP @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(641,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( c_Type_Otype_OFun @ A @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ F ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ F ) @ E ) @ B ) ) @ C ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(2268,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( c_Type_Otype_OFun @ A @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ F ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ F ) @ E ) @ B ) ) @ C ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(264,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1397,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(2498,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(948,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(321,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
| ( D = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1534,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
| ( D = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(96,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(1017,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(2460,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(249,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_1) ).
thf(1361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(664,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_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(2323,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_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(720,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ A @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ ( tc_prod @ A @ B ) ) ) ) @ ( c_Pair @ A @ B ) ) ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ A @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ ( tc_prod @ A @ B ) ) ) ) @ ( c_Pair @ A @ B ) ) ) ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq2_0) ).
thf(2455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ A @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ ( tc_prod @ A @ B ) ) ) ) @ ( c_Pair @ A @ B ) ) ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBC @ B @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_prod @ A @ B ) ) @ ( tc_fun @ B @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ A @ B ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ ( tc_prod @ A @ B ) ) ) ) @ ( c_Pair @ A @ B ) ) ) ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(560,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ E @ D ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__less_0) ).
thf(2080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ E @ D ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(2349,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__ball__eq_0) ).
thf(1889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(106,axiom,
! [A: $i] :
( ( c_Predicate_OPowp @ A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Powp__def_0) ).
thf(1039,plain,
! [A: $i] :
( ( c_Predicate_OPowp @ A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__Inf_0) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(40,axiom,
! [A: $i] : ( class_Orderings_Obot @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Orderings_Obot) ).
thf(884,plain,
! [A: $i] : ( class_Orderings_Obot @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1329,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)],[235]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
thf(1739,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(48,axiom,
! [A: $i] : ( class_Lattices_Olattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Lattices_Olattice) ).
thf(901,plain,
! [A: $i] : ( class_Lattices_Olattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(1075,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)],[123]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1810,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1791,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)],[434]) ).
thf(760,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2551,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(562,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(2085,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(997,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(985,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)],[84]) ).
thf(735,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_split @ A @ D @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ E ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_0) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_split @ A @ D @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ E ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(514,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
thf(1974,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(724,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__fin__Sup_0) ).
thf(2465,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(473,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(277,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1429,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_0) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_some__sym__eq__trivial_0) ).
thf(1324,plain,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(743,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 ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ H @ A @ I @ D @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Osup__compl__top_0) ).
thf(2504,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 ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ H @ A @ I @ D @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(297,axiom,
( ( c_FunDef_OTHE__default @ v_d @ v_P @ t_a )
= ( c_HOL_OIf @ ( hAPP @ ( c_Ex @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) ) ) ) ) @ ( c_The @ v_P @ t_a ) @ v_d @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_THE__default__def__raw_0) ).
thf(1478,plain,
( ( c_FunDef_OTHE__default @ v_d @ v_P @ t_a )
= ( c_HOL_OIf @ ( hAPP @ ( c_Ex @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) ) ) ) ) @ ( c_The @ v_P @ t_a ) @ v_d @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Fun_Oid @ B ) )
= ( c_Fun_Oid @ C ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__id_0) ).
thf(1249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Fun_Oid @ B ) )
= ( c_Fun_Oid @ C ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(748,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Oset @ B @ C ) )
= ( c_List_Ofoldl @ D @ E @ B @ C @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ D @ E @ J @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__set__fold_0) ).
thf(2519,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Oset @ B @ C ) )
= ( c_List_Ofoldl @ D @ E @ B @ C @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ D @ E @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(323,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1539,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Oorder_Omono @ B @ C @ A )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ A ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ C ) @ ( c_All @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBS @ C @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( c_COMBC @ C @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBB @ A @ tc_bool @ C ) ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( c_lessequals @ A ) ) ) ) ) @ ( c_COMBI @ ( tc_fun @ C @ A ) ) ) ) ) ) )
| ~ ( c_Orderings_Oorder @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Omono__def__raw_0) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Oorder_Omono @ B @ C @ A )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ A ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ C ) @ ( c_All @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBS @ C @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( c_COMBC @ C @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ A ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ C @ A ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( c_COMBB @ A @ tc_bool @ C ) ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( c_lessequals @ A ) ) ) ) ) @ ( c_COMBI @ ( tc_fun @ C @ A ) ) ) ) ) ) )
| ~ ( c_Orderings_Oorder @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I1_J_1) ).
thf(1231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__compr_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(1932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(90,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ B ) ) @ C ) @ C @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ E ) @ B @ F @ G @ H @ A )
| ~ ( c_Lattices_Oboolean__algebra @ I @ C @ D @ E @ F @ B @ H @ G @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odual__boolean__algebra_0) ).
thf(1002,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ B ) ) @ C ) @ C @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ E ) @ B @ F @ G @ H @ A )
| ~ ( c_Lattices_Oboolean__algebra @ I @ C @ D @ E @ F @ B @ H @ G @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Least__le_0) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(197,axiom,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUPR__def__raw_0) ).
thf(1246,plain,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1857,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1318,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)],[229]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ B @ A ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(938,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)],[64]) ).
thf(758,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ E @ D ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ E ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bounded__ex_0) ).
thf(2546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ E @ D ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ E ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ A ) ) @ B @ tc_Lambda_OdB ) )
| ~ ( c_Type_Otypings @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lists__typings_0) ).
thf(1779,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ A ) ) @ B @ tc_Lambda_OdB ) )
| ~ ( c_Type_Otypings @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(544,axiom,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ c_InductTermi_OIT ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_Ohyps_0) ).
thf(2043,plain,
hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ c_InductTermi_OIT ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(714,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(2440,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(621,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I5_J_0) ).
thf(2221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(100,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 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1026,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 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(615,axiom,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_some__eq__trivial_0) ).
thf(2208,plain,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter_Osimps_I1_J_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(550,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(2057,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(398,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I9_J_0) ).
thf(1712,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(113,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1054,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__less_1) ).
thf(1035,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(683,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ D @ tc_bool ) @ E ) ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ A @ E @ F @ G @ H @ I @ J @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__Inf_0) ).
thf(2368,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ D @ tc_bool ) @ E ) ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ A @ E @ F @ G @ H @ I @ J @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__listsp__conv__set_1) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_List_Osko__List__Xin__listsp__conv__set__1__1 @ A @ B @ C ) ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(707,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_COMBK @ B @ B ) @ ( hAPP @ C @ ( hAPP @ D @ E ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__def_0) ).
thf(2423,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_COMBK @ B @ B ) @ ( hAPP @ C @ ( hAPP @ D @ E ) ) ) ) @ E )
= ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ A @ D @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(211,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ A ) @ C )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(1278,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ A ) @ C )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(150,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ E ) @ F @ G @ H @ I @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ D @ E @ G @ F @ I @ H @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(1135,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ E ) @ F @ G @ H @ I @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ D @ E @ G @ F @ I @ H @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(525,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(2001,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)],[525]) ).
thf(508,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1959,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(1219,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(209,axiom,
( ~ ( class_Orderings_Oorder @ t_a )
| ~ ( class_Orderings_Oorder @ t_b )
| ( ( c_Orderings_Oorder__class_Ostrict__mono @ v_f @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( c_HOL_Oord__class_Oless @ t_a ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_HOL_Oord__class_Oless @ t_b ) ) @ v_f ) ) ) @ v_f ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__def__raw_0) ).
thf(1273,plain,
( ~ ( class_Orderings_Oorder @ t_a )
| ~ ( class_Orderings_Oorder @ t_b )
| ( ( c_Orderings_Oorder__class_Ostrict__mono @ v_f @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( c_HOL_Oord__class_Oless @ t_a ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_HOL_Oord__class_Oless @ t_b ) ) @ v_f ) ) ) @ v_f ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(414,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_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1747,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_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(495,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_List_Oset @ B @ A ) )
= ( c_List_Ofoldl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__set__fold_0) ).
thf(1927,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_List_Oset @ B @ A ) )
= ( c_List_Ofoldl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__singleton_0) ).
thf(2602,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OInf__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Inf2__distrib_0) ).
thf(2028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OInf__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBS @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ A @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ A @ A ) ) @ ( tc_fun @ A @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(686,axiom,
class_Orderings_Owellorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Owellorder) ).
thf(2376,plain,
class_Orderings_Owellorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Collect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) @ tc_bool ) @ C ) @ ( c_in @ ( tc_prod @ B @ C ) ) ) @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton_0) ).
thf(1631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Collect @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_prod @ B @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) @ tc_bool ) @ C ) @ ( c_in @ ( tc_prod @ B @ C ) ) ) @ ( hAPP @ ( c_Pair @ B @ C ) @ D ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(628,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ I @ J @ K )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__eq__compl__iff_0) ).
thf(2235,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ I @ J @ K )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ C ) ) ) @ D ) @ A @ B @ tc_bool ) )
= ( c_Product__Type_OSigma @ ( hAPP @ ( c_Collect @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Collect @ B ) @ D ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__split_0) ).
thf(2144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ C ) ) ) @ D ) @ A @ B @ tc_bool ) )
= ( c_Product__Type_OSigma @ ( hAPP @ ( c_Collect @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Collect @ B ) @ D ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(422,axiom,
( ( c_Predicate_Osingleton @ v_dfault @ v_A @ t_a )
= ( c_HOL_OIf @ ( hAPP @ ( c_Ex @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) ) ) ) ) @ ( c_The @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) @ t_a ) @ ( hAPP @ v_dfault @ c_Product__Type_OUnity ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__def__raw_0) ).
thf(1764,plain,
( ( c_Predicate_Osingleton @ v_dfault @ v_A @ t_a )
= ( c_HOL_OIf @ ( hAPP @ ( c_Ex @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) ) ) ) @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) ) ) ) ) @ ( c_The @ ( hAPP @ ( c_Predicate_Oeval @ t_a ) @ v_A ) @ t_a ) @ ( hAPP @ v_dfault @ c_Product__Type_OUnity ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(703,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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(2413,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)],[703]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(2033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(2149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1007,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(18,axiom,
! [A: $i] : ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Complete__Lattice_Ocomplete__lattice) ).
thf(843,plain,
! [A: $i] : ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(750,axiom,
v_n____ != v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_False_0) ).
thf(2525,plain,
v_n____ != v_i____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(2188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_1) ).
thf(1752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(510,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
thf(1965,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I2_J_0) ).
thf(1226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Predicate_Opred_OPred @ A @ B )
!= ( c_Predicate_Opred_OPred @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred_Oinject_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Predicate_Opred_OPred @ A @ B )
!= ( c_Predicate_Opred_OPred @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ B @ C ) ) @ ( c_List_Oset @ E @ C ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__map__eq__map_0) ).
thf(975,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ B @ C ) ) @ ( c_List_Oset @ E @ C ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(623,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(2225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(477,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1884,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ E ) @ F ) )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(436,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(393,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I9_J_0) ).
thf(1701,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(152,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I5_J_0) ).
thf(1139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(609,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ B @ C @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__bot__eq_0) ).
thf(2193,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ B @ C @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(936,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)],[63]) ).
thf(665,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I10_J_0) ).
thf(2326,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(226,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_ea______ ) @ v_ua______ ) @ v_T____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
thf(1312,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ v_ea______ ) @ v_ua______ ) @ v_T____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1865,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
= ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1733,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
= ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(2055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(596,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(2166,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(651,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(657,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_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_0) ).
thf(2308,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_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olinorder_OMin @ C @ D @ E ) )
= ( c_Finite__Set_Olinorder_OMin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_OrderedGroup_Oordered__ab__semigroup__add @ A @ C @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ordered__ab__semigroup__add_Oadd__Min__commute_0) ).
thf(1371,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olinorder_OMin @ C @ D @ E ) )
= ( c_Finite__Set_Olinorder_OMin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_OrderedGroup_Oordered__ab__semigroup__add @ A @ C @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oless__le_1) ).
thf(2557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Onth @ ( c_List_Omap @ A @ B @ C @ D ) @ D ) @ E )
= ( hAPP @ A @ ( hAPP @ ( c_List_Onth @ B @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ E ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__map_0) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Onth @ ( c_List_Omap @ A @ B @ C @ D ) @ D ) @ E )
= ( hAPP @ A @ ( hAPP @ ( c_List_Onth @ B @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ E ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(728,axiom,
( ( c_Relation_Osingle__valued @ v_r @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_b ) @ ( c_All @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) ) @ t_a ) @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) ) @ ( c_fequal @ t_b ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__def__raw_0) ).
thf(2474,plain,
( ( c_Relation_Osingle__valued @ v_r @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ t_b ) @ ( c_All @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) ) @ t_a ) @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_b @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ t_b @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_b ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ ( tc_fun @ t_b @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_b @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_prod @ t_a @ t_b ) ) @ ( tc_fun @ t_b @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_b ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_b ) @ tc_bool ) @ tc_bool ) @ t_b ) @ ( c_in @ ( tc_prod @ t_a @ t_b ) ) ) ) @ ( c_Pair @ t_a @ t_b ) ) ) ) @ v_r ) ) ) ) ) @ ( c_fequal @ t_b ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(1638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(1224,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(2573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(247,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olattice_OSup__fin @ C @ D @ E ) )
= ( c_Finite__Set_Olattice_OSup__fin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Oinf__Sup1__distrib_0) ).
thf(1356,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olattice_OSup__fin @ C @ D @ E ) )
= ( c_Finite__Set_Olattice_OSup__fin @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(745,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_1) ).
thf(2510,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(2538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(2151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(403,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1722,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(425,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__monoD_0) ).
thf(1771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(388,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Odistrib__lattice @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ C ) @ D @ E @ A )
| ~ ( c_Lattices_Odistrib__lattice @ B @ C @ E @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Odual__distrib__lattice_0) ).
thf(1690,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Odistrib__lattice @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ C ) @ D @ E @ A )
| ~ ( c_Lattices_Odistrib__lattice @ B @ C @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Inf__absorb_0) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ C @ A ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ C ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_1) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ C ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(673,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(2346,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_0) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(730,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(2478,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(704,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ A ) @ B ) @ C ) @ D ) @ E )
= ( hAPP @ B @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(2415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ A ) @ B ) @ C ) @ D ) @ E )
= ( hAPP @ B @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1894,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(797,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ A ) @ B ) @ C ) ) @ ( c_Lambda_Olift @ D @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(2637,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ A ) @ B ) @ C ) ) @ ( c_Lambda_Olift @ D @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__def_0) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1806,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(647,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(2257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(346,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1589,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(632,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) @ B @ C )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(2246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) @ B @ C )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ C ) ) ) ) @ ( hAPP @ ( c_fequal @ B ) @ D ) ) @ A @ B @ tc_bool ) @ ( tc_prod @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Eps__split__eq_0) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_COMBB @ tc_bool @ tc_bool @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ C ) ) ) ) @ ( hAPP @ ( c_fequal @ B ) @ D ) ) @ A @ B @ tc_bool ) @ ( tc_prod @ A @ B ) )
= ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
thf(1043,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ole__neq__trans_0) ).
thf(1801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Omap @ B @ C @ D @ A ) )
| ( C
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(167,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 )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ A ) @ ( c_Fun_Oid @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ D ) ) )
| ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__reindex__id_0) ).
thf(1175,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 )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ A @ A ) @ ( c_Fun_Oid @ A ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ B @ A ) @ D ) ) )
| ~ ( c_Fun_Oinj__on @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(603,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(2182,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1339,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_someI_0) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(580,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ B @ C ) ) @ ( c_List_Oset @ E @ C ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__inj__on_0) ).
thf(2129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_List_Oset @ B @ C ) ) @ ( c_List_Oset @ E @ C ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__disj__eq_0) ).
thf(1731,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1,negated_conjecture,
~ ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(799,plain,
~ ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_All @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_bool @ tc_Type_Otype ) @ ( c_All @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_All @ tc_nat ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( c_COMBS @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Type_Otype ) @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Type_Otype ) @ ( c_COMBS @ tc_nat @ tc_bool @ tc_bool ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_bool @ tc_bool ) ) @ tc_Type_Otype ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_nat ) @ c_implies ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ tc_nat ) @ c_Type_Otyping ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_nat @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_nat @ tc_Type_Otype @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) ) @ ( c_Type_Oshift @ tc_Type_Otype ) ) ) @ v_T____ ) ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) @ c_InductTermi_OIT ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBS @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( c_COMBB @ tc_bool @ tc_bool @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Lambda_OdB ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_nat @ tc_Type_Otype ) @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) ) @ ( tc_fun @ tc_Type_Otype @ ( tc_fun @ tc_Lambda_OdB @ tc_bool ) ) @ ( tc_fun @ tc_nat @ tc_Type_Otype ) ) @ ( c_COMBC @ tc_Lambda_OdB @ tc_Type_Otype @ tc_bool ) ) @ c_Type_Otyping ) ) @ v_T____ ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ ( tc_fun @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Lambda_OdB ) @ ( hAPP @ ( c_COMBB @ tc_Lambda_OdB @ tc_bool @ tc_nat ) @ c_InductTermi_OIT ) ) ) @ c_Lambda_Osubst ) ) ) ) ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Type_Otype @ tc_bool ) @ tc_bool @ tc_Lambda_OdB ) @ ( c_Ex @ tc_Type_Otype ) ) @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) ) ) @ v_rs____ @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(457,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1838,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(75,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(2289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(116,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1061,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(449,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I9_J_0) ).
thf(1820,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ A ) @ ( c_List_Oset @ C @ B ) ) @ D )
= ( c_List_Ofoldl @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) @ D ) ) @ ( c_Orderings_Obot__class_Obot @ A ) @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUPR__set__fold_0) ).
thf(1667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ A ) @ ( c_List_Oset @ C @ B ) ) @ D )
= ( c_List_Ofoldl @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) @ D ) ) @ ( c_Orderings_Obot__class_Obot @ A ) @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(602,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(2180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(125,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Olattice_OInf__fin @ B @ C @ D ) ) @ ( c_Finite__Set_Olattice_OInf__fin @ B @ E @ D ) )
= ( c_Finite__Set_Olattice_OInf__fin @ B @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBS @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBB @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ D @ tc_bool @ D ) ) @ ( c_fequal @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ tc_bool @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ E ) ) ) ) ) ) @ D ) )
| ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Osup__Inf2__distrib_0) ).
thf(1080,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Olattice_OInf__fin @ B @ C @ D ) ) @ ( c_Finite__Set_Olattice_OInf__fin @ B @ E @ D ) )
= ( c_Finite__Set_Olattice_OInf__fin @ B @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBS @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBB @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ D @ tc_bool @ D ) ) @ ( c_fequal @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ tc_bool @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ E ) ) ) ) ) ) @ D ) )
| ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(795,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ A @ B ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
thf(2632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ ( hAPP @ ( c_COMBK @ A @ B ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(779,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2593,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(98,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__UN__flatten_0) ).
thf(1022,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(634,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(2252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(732,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_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2481,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_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(369,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) ) @ D ) )
| ~ ( hBOOL @ ( c_Relation_Otrans @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
thf(1643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) ) @ D ) )
| ~ ( hBOOL @ ( c_Relation_Otrans @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__mono_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(2156,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(57,axiom,
! [A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Lattices_Obounded__lattice) ).
thf(922,plain,
! [A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(2069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(558,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(2075,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(705,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Olattice_OInf__fin @ A @ B @ C )
= ( hAPP @ D @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ E @ F @ G @ A @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__fin__Inf_0) ).
thf(2418,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Olattice_OInf__fin @ A @ B @ C )
= ( hAPP @ D @ B ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ E @ F @ G @ A @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1841,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I5_J_0) ).
thf(1699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(2212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(959,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)],[72]) ).
thf(284,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_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1445,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_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(791,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(2620,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(33,axiom,
! [A: $i] : ( class_Lattices_Oupper__semilattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Lattices_Oupper__semilattice) ).
thf(868,plain,
! [A: $i] : ( class_Lattices_Oupper__semilattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(427,axiom,
! [A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( c_Lattices_Odistrib__lattice @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__distrib__lattice_0) ).
thf(1775,plain,
! [A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( c_Lattices_Odistrib__lattice @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(2244,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(280,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olinorder_OMax @ C @ D @ E ) )
= ( c_Finite__Set_Olinorder_OMax @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_OrderedGroup_Oordered__ab__semigroup__add @ A @ C @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ordered__ab__semigroup__add_Oadd__Max__commute_0) ).
thf(1435,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Olinorder_OMax @ C @ D @ E ) )
= ( c_Finite__Set_Olinorder_OMax @ C @ ( hAPP @ ( c_Collect @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBS @ E @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ E @ ( tc_fun @ tc_bool @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ E ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ tc_bool ) @ ( tc_fun @ ( tc_fun @ E @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( c_COMBB @ E @ tc_bool @ E ) ) @ ( c_fequal @ E ) ) ) @ ( hAPP @ A @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ E @ tc_bool ) @ tc_bool ) @ ( c_in @ E ) ) @ D ) ) ) ) @ E ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_OrderedGroup_Oordered__ab__semigroup__add @ A @ C @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(754,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2535,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)],[754]) ).
thf(568,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ E @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(2101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ E @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(405,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1726,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(250,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I4_J_0) ).
thf(1364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(693,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_1) ).
thf(2390,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(305,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(1496,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(655,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(2303,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(135,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ F ) )
= ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ C @ E ) @ A ) @ D ) @ E @ C ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(1102,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ F ) )
= ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ C @ E ) @ A ) @ D ) @ E @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1626,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1467,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)],[293]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(2471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(274,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ A @ B ) )
= B )
| ~ ( c_Lattices_Oboolean__algebra @ C @ A @ D @ E @ F @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odouble__compl_0) ).
thf(1420,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ A @ B ) )
= B )
| ~ ( c_Lattices_Oboolean__algebra @ C @ A @ D @ E @ F @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(2124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(794,axiom,
( ~ ( class_Orderings_Oorder @ t_a )
| ~ ( class_Orderings_Oorder @ t_b )
| ( ( c_Orderings_Oorder__class_Omono @ v_f @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( c_lessequals @ t_a ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_lessequals @ t_b ) ) @ v_f ) ) ) @ v_f ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__def__raw_0) ).
thf(2629,plain,
( ~ ( class_Orderings_Oorder @ t_a )
| ~ ( class_Orderings_Oorder @ t_b )
| ( ( c_Orderings_Oorder__class_Omono @ v_f @ t_a @ t_b )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( c_lessequals @ t_a ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_a ) @ ( c_lessequals @ t_b ) ) @ v_f ) ) ) @ v_f ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(1990,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(781,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(2597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(823,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(774,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(2582,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(111,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(1049,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1662,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(788,axiom,
( ( c_Relation_Otrans @ v_r @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def__raw_0) ).
thf(2614,plain,
( ( c_Relation_Otrans @ v_r @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ ( tc_fun @ tc_bool @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_COMBC @ t_a @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_prod @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) ) @ t_a ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ t_a @ t_a ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ t_a @ t_a ) @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ ( tc_prod @ t_a @ t_a ) ) ) ) @ ( c_Pair @ t_a @ t_a ) ) ) ) @ v_r ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(566,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(2096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Orderings_Oorder @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oeq__iff_0) ).
thf(2318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Orderings_Oorder @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(642,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(2271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(766,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(2564,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(328,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert__distrib_0) ).
thf(1547,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(653,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ C ) @ D ) @ C @ B )
!= ( c_Product__Type_OSigma @ E @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ C ) @ D ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ F ) @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(2298,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ C ) @ D ) @ C @ B )
!= ( c_Product__Type_OSigma @ E @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ C ) @ D ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ F ) @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(25,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Orderings_Oorder) ).
thf(855,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(2397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(355,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__INT__eq_0) ).
thf(1611,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(412,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(1743,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(42,axiom,
! [A: $i] : ( class_Orderings_Otop @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Orderings_Otop) ).
thf(887,plain,
! [A: $i] : ( class_Orderings_Otop @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(336,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1566,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(600,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Relation_OImage @ A @ B @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__UN_0) ).
thf(2175,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Relation_OImage @ A @ B @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(700,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ) @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UN__distrib2_0) ).
thf(2407,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(460,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_1) ).
thf(1845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Sup__absorb_0) ).
thf(2513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(767,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Set_Oimage @ A @ B @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__UN_0) ).
thf(2567,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Set_Oimage @ A @ B @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(777,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ C ) @ B ) ) @ D ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( c_Relation_Ototal__on @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(2588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ C ) @ B ) ) @ D ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( c_Relation_Ototal__on @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= B )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__id__conv_0) ).
thf(1941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= B )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(199,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I7_J_0) ).
thf(1252,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__UN__eq_0) ).
thf(2160,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(1499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(768,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(2569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(400,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1716,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(171,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ E @ B @ F @ G ) )
| ( ( hAPP @ ( hAPP @ E @ A ) @ C )
= ( hAPP @ ( hAPP @ E @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_update__accessor__congruence__foldE_0) ).
thf(1186,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( c_Record_Oiso__tuple__update__accessor__cong__assist @ E @ B @ F @ G ) )
| ( ( hAPP @ ( hAPP @ E @ A ) @ C )
= ( hAPP @ ( hAPP @ E @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(204,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1262,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(669,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ C @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ F ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(2337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E ) @ F )
= ( hAPP @ C @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ F ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1901,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
thf(1085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(545,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ D ) @ B ) @ E ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(2044,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ D ) @ B ) @ E ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(238,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(1336,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( c_lessequals @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__Sup_0) ).
thf(2468,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( c_lessequals @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(221,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(1300,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(16,axiom,
! [A: $i] : ( class_Lattices_Olower__semilattice @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__Lattices_Olower__semilattice) ).
thf(840,plain,
! [A: $i] : ( class_Lattices_Olower__semilattice @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Predicate_Oeval @ A ) @ B )
!= ( hAPP @ ( c_Predicate_Oeval @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__inject_0) ).
thf(1785,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Predicate_Oeval @ A ) @ B )
!= ( hAPP @ ( c_Predicate_Oeval @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Collect @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(2276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Collect @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(951,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)],[69]) ).
thf(782,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(2599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ D )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBK @ A @ B ) @ C ) @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(757,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(772,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2579,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(308,axiom,
! [A: $i] :
( ( c_Orderings_Oord_OLeast @ A @ v_P @ t_a )
= ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ A ) ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ord_OLeast__def__raw_0) ).
thf(1504,plain,
! [A: $i] :
( ( c_Orderings_Oord_OLeast @ A @ v_P @ t_a )
= ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ A ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1717,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(476,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 ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ A @ H @ D @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Oinf__compl__bot_0) ).
thf(1881,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 ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ A @ H @ D @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(27,axiom,
! [B: $i,A: $i] : ( c_Finite__Set_Ofinite @ ( c_List_Oset @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__set_0) ).
thf(859,plain,
! [B: $i,A: $i] : ( c_Finite__Set_Ofinite @ ( c_List_Oset @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(2411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(741,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(2500,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__all__eq_0) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(153,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(1141,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( 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)],[153]) ).
thf(708,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I7_J_0) ).
thf(2426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__empty__conv_0) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofilter @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ A ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp__infI_0) ).
thf(2279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_List_Olistsp @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ A ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_List_Olistsp @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(678,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__le__Sup_0) ).
thf(2357,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olattice__class_OInf__fin @ B @ A ) ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ B @ A ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
thf(1972,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(662,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(2320,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( hAPP @ ( c_Set_Oimage @ D @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( hAPP @ ( c_Set_Oimage @ D @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(344,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1585,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OSup__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Sup1__distrib_0) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Finite__Set_Olattice__class_OSup__fin @ C @ A ) )
= ( c_Finite__Set_Olattice__class_OSup__fin @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBS @ A @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ ( tc_fun @ tc_bool @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_COMBB @ A @ tc_bool @ A ) ) @ ( c_fequal @ A ) ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(194,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1240,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(991,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)],[86]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Recdef_Oadm__wf @ A @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ ( tc_fun @ B @ B ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ ( tc_fun @ B @ B ) @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ C ) ) @ ( c_COMBS @ B @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ C ) @ ( tc_fun @ B @ C ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) ) @ ( c_Recdef_Ocut @ B @ C ) ) @ A ) ) ) ) @ ( c_COMBI @ B ) ) @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_adm__lemma_0) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Recdef_Oadm__wf @ A @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ ( tc_fun @ B @ B ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ ( tc_fun @ B @ B ) @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ C ) ) @ ( c_COMBS @ B @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ C ) @ ( tc_fun @ B @ C ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) @ ( tc_fun @ B @ ( tc_fun @ B @ C ) ) ) @ ( c_Recdef_Ocut @ B @ C ) ) @ A ) ) ) ) @ ( c_COMBI @ B ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(530,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ B @ C @ D @ E )
= ( hAPP @ ( c_Collect @ ( tc_prod @ C @ E ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) ) @ C ) @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ C @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) @ D ) @ ( c_in @ ( tc_prod @ C @ D ) ) ) ) @ ( c_Pair @ C @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ E ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) @ D ) @ ( c_in @ ( tc_prod @ D @ E ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ E @ ( tc_prod @ D @ E ) ) @ ( c_Pair @ D @ E ) ) ) ) ) @ B ) ) ) @ C @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__def_0) ).
thf(2013,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ B @ C @ D @ E )
= ( hAPP @ ( c_Collect @ ( tc_prod @ C @ E ) ) @ ( c_split @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ E ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ E @ ( tc_fun @ D @ tc_bool ) ) ) @ C ) @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ C @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ C @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) @ tc_bool ) @ D ) @ ( c_in @ ( tc_prod @ C @ D ) ) ) ) @ ( c_Pair @ C @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ E ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) ) @ E ) @ ( hAPP @ ( c_COMBB @ ( tc_prod @ D @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) @ tc_bool ) @ D ) @ ( c_in @ ( tc_prod @ D @ E ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ E @ ( tc_prod @ D @ E ) ) @ ( c_Pair @ D @ E ) ) ) ) ) @ B ) ) ) @ C @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(721,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ F ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2E_0) ).
thf(2458,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ A ) @ F ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(731,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(2479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_1) ).
thf(2088,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(290,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1459,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_1) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(504,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ D @ E ) @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
thf(1949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ D @ E ) @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(658,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_1) ).
thf(2310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(787,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2611,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)],[787]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ C @ A @ B @ tc_bool ) ) @ A @ B ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Collect__split_0) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( hAPP @ ( c_Collect @ ( tc_prod @ A @ B ) ) @ ( c_split @ C @ A @ B @ tc_bool ) ) @ A @ B ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_Ex @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(556,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__mono__less__eq_1) ).
thf(2071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Orderings_Oorder @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Ostrict__mono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(524,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ E @ B @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__sup_0) ).
thf(1998,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ E @ B @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(793,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 @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ F ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
thf(2626,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 @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ F ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(491,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1918,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(455,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(1834,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(489,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_1) ).
thf(1913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oantisym_0) ).
thf(1412,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).
thf(2215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(736,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Ofilter @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__filter__less_0) ).
thf(2490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Ofilter @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(1189,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)],[172]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(671,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(2342,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1289,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)],[216]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Oappend @ B @ C @ D ) @ D @ E )
= ( c_List_Oappend @ ( c_List_Omap @ A @ B @ D @ E ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(715,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib_0) ).
thf(2443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(296,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
thf(1476,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(363,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UN__distrib_0) ).
thf(1629,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(413,axiom,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1745,plain,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(535,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(2026,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_u____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(710,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 @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
thf(2431,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 @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(638,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(2262,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(778,axiom,
( ( c_lessequals @ tc_bool )
= c_implies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__bool__def__raw_0) ).
thf(2591,plain,
( ( c_lessequals @ tc_bool )
= c_implies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_filter__append_0) ).
thf(813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofilter @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Ofilter @ A @ B @ D ) @ ( c_List_Ofilter @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(2594,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(2098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(485,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1903,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(582,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ A ) @ D ) @ C ) ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(2135,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ A ) @ D ) @ C ) ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ E ) @ B ) @ D ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(310,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_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1508,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_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1244,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)],[196]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_1) ).
thf(1822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(467,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ F ) @ D ) @ E ) )
| ( ( hAPP @ C @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ G ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(1861,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ C ) @ D ) @ E )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ A @ B ) @ F ) @ D ) @ E ) )
| ( ( hAPP @ C @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ G ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1491,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)],[303]) ).
thf(690,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(2384,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(428,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ E ) ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_0) ).
thf(1777,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ E ) ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(723,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(2462,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(224,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ G @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ G @ B ) @ H ) @ D ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ G ) @ C ) @ H ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1308,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ B ) @ C ) @ D ) ) @ ( c_Relation_Orel__comp @ E @ F @ A @ G @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ G @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ G @ B ) @ H ) @ D ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ G ) @ C ) @ H ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(2120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(660,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(738,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(2494,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(792,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/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(2623,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)],[792]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(697,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(2399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(543,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un__distrib_0) ).
thf(2041,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(771,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(2576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(554,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( c_Type_Otype_OFun @ A @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ F ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ F ) @ E ) @ A ) ) @ C ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(2066,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( c_Type_Otype_OFun @ A @ B ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ C ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ F ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ F ) @ E ) @ A ) ) @ C ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) ) @ C ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(2362,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) ) @ C ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ A ) @ B ) @ C ) @ D ) @ C )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(2162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ A ) @ B ) @ C ) @ D ) @ C )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(2183,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ C ) @ D )
= ( hAPP @ ( c_List_Onth @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append_0) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ C ) @ D )
= ( hAPP @ ( c_List_Onth @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(625,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(2230,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)],[625]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(2036,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ C ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 @ C @ D @ B @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bounded__ex_1) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ C ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1 @ C @ D @ B @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_0) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(2421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
= ( hAPP @ ( c_Set_Oimage @ A @ C @ D ) @ ( c_List_Oset @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__map_0) ).
thf(2003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oset @ ( c_List_Omap @ A @ B @ C @ D ) @ D )
= ( hAPP @ ( c_Set_Oimage @ A @ C @ D ) @ ( c_List_Oset @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(691,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(2233,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(263,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 @ D ) @ E ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).
thf(1395,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 @ D ) @ E ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(749,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(2522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(474,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1876,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(577,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2123,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Relation_OImage @ A @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__eq__UN_0) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Relation_OImage @ A @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Set_Oinsert @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(2604,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(2008,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(519,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1986,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_2) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(32,axiom,
! [A: $i] : ( class_HOL_Oord @ ( tc_Predicate_Opred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Predicate__Opred__HOL_Oord) ).
thf(867,plain,
! [A: $i] : ( class_HOL_Oord @ ( tc_Predicate_Opred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1757,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(466,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/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1859,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)],[466]) ).
thf(446,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_H____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
thf(1816,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Type_Oshift @ tc_Type_Otype ) @ v_e____ ) @ v_i____ ) @ v_T____ ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) @ v_rs____ @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ v_T_H____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(668,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(2334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(2186,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(807,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_List_Oset @ B @ A ) )
= ( c_List_Ofoldl @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__set__fold_0) ).
thf(1693,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_List_Oset @ B @ A ) )
= ( c_List_Ofoldl @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) @ D ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2I_0) ).
thf(1561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) @ D ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(682,axiom,
! [A: $i] :
( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__empty_1) ).
thf(2366,plain,
! [A: $i] :
( ( c_List_Oset @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(564,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(480,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1891,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(670,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ F ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(2340,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Relation_OImage @ C @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ D @ A ) @ F ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(612,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Lattices_Oboolean__algebra @ A @ B @ C @ D @ E @ F @ ( hAPP @ ( hAPP @ E @ G ) @ H ) @ ( hAPP @ ( hAPP @ F @ G ) @ H ) @ I )
| ( ( hAPP @ B @ G )
= H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__unique_0) ).
thf(2201,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Lattices_Oboolean__algebra @ A @ B @ C @ D @ E @ F @ ( hAPP @ ( hAPP @ E @ G ) @ H ) @ ( hAPP @ ( hAPP @ F @ G ) @ H ) @ I )
| ( ( hAPP @ B @ G )
= H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(801,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(166,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Olattice_OSup__fin @ B @ C @ D ) ) @ ( c_Finite__Set_Olattice_OSup__fin @ B @ E @ D ) )
= ( c_Finite__Set_Olattice_OSup__fin @ B @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBS @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBB @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ D @ tc_bool @ D ) ) @ ( c_fequal @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ tc_bool @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ E ) ) ) ) ) ) @ D ) )
| ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Oinf__Sup2__distrib_0) ).
thf(1172,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Olattice_OSup__fin @ B @ C @ D ) ) @ ( c_Finite__Set_Olattice_OSup__fin @ B @ E @ D ) )
= ( c_Finite__Set_Olattice_OSup__fin @ B @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_Ex @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBS @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBS @ D @ tc_bool @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) ) @ D ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ ( tc_fun @ tc_bool @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ ( c_COMBB @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ D @ tc_bool @ D ) ) @ ( c_fequal @ D ) ) ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_bool @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ tc_bool @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ E ) ) ) ) ) ) @ D ) )
| ( E
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(103,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(1033,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(1710,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).
thf(2223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_COMBK @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) )
= D )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(533,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oless__le_2) ).
thf(2021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(243,axiom,
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ v_upd @ v_acc @ t_a @ t_b )
= ( hAPP @ ( hAPP @ c_and @ ( hAPP @ ( c_All @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ t_a ) ) @ ( c_All @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( c_COMBS @ t_b @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) @ ( c_fequal @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( c_COMBS @ t_b @ t_b @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_a @ t_a ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ t_b ) @ v_upd ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ t_a ) @ ( tc_fun @ t_b @ ( tc_fun @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ t_a @ ( tc_fun @ t_a @ t_a ) @ t_b ) @ ( c_COMBK @ t_a @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_a ) @ ( tc_fun @ t_b @ t_a ) ) @ ( c_COMBB @ t_a @ t_a @ t_b ) ) @ v_acc ) ) ) ) ) @ ( c_COMBI @ t_b ) ) ) ) ) @ v_upd ) ) ) ) @ ( hAPP @ ( c_All @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_b @ t_b @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) @ ( c_fequal @ t_b ) ) @ ( hAPP @ v_upd @ ( c_Fun_Oid @ t_a ) ) ) ) @ ( c_COMBI @ t_b ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__def__raw_0) ).
thf(1346,plain,
( ( c_Record_Oiso__tuple__update__accessor__cong__assist @ v_upd @ v_acc @ t_a @ t_b )
= ( hAPP @ ( hAPP @ c_and @ ( hAPP @ ( c_All @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ t_a ) ) @ ( c_All @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( c_COMBS @ t_b @ t_b @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) @ ( c_fequal @ t_b ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ ( tc_fun @ t_b @ t_b ) @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( c_COMBS @ t_b @ t_b @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ ( tc_fun @ t_a @ t_a ) ) @ ( tc_fun @ t_b @ ( tc_fun @ t_b @ t_b ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_b ) @ t_b ) @ v_upd ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ t_a ) @ ( tc_fun @ t_b @ ( tc_fun @ t_a @ t_a ) ) @ ( tc_fun @ t_a @ t_a ) ) @ ( hAPP @ ( c_COMBB @ t_a @ ( tc_fun @ t_a @ t_a ) @ t_b ) @ ( c_COMBK @ t_a @ t_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_a ) @ ( tc_fun @ t_b @ t_a ) @ ( tc_fun @ t_b @ t_a ) ) @ ( c_COMBB @ t_a @ t_a @ t_b ) ) @ v_acc ) ) ) ) ) @ ( c_COMBI @ t_b ) ) ) ) ) @ v_upd ) ) ) ) @ ( hAPP @ ( c_All @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_b @ t_b @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ t_b @ tc_bool ) @ t_b ) @ ( c_fequal @ t_b ) ) @ ( hAPP @ v_upd @ ( c_Fun_Oid @ t_a ) ) ) ) @ ( c_COMBI @ t_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(553,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oeq__iff_2) ).
thf(2063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(207,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ~ ( class_Lattices_Olower__semilattice @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__inf_0) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ~ ( class_Lattices_Olower__semilattice @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1152,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)],[158]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1582,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)],[343]) ).
thf(775,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ C @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__lattice_Oinf__sup__distrib1_0) ).
thf(2583,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Lattices_Odistrib__lattice @ F @ G @ A @ C @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(744,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(2507,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(734,axiom,
( ~ ( class_HOL_Oord @ t_a )
| ( ( c_Orderings_Oord__class_OLeast @ v_P @ t_a )
= ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ ( c_lessequals @ t_a ) ) ) ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Least__def__raw_0) ).
thf(2484,plain,
( ~ ( class_HOL_Oord @ t_a )
| ( ( c_Orderings_Oord__class_OLeast @ v_P @ t_a )
= ( c_The @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ v_P ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_a ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_a ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ v_P ) ) ) @ ( c_lessequals @ t_a ) ) ) ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(360,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ E ) @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ E ) @ A ) ) @ F ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ F @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(1621,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ E ) @ B ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ C @ D ) @ E ) @ A ) ) @ F ) )
| ~ ( hBOOL @ ( c_Relation_Osingle__valued @ F @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( c_Predicate_Opred_OPred @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pred__eval_0) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ( c_Predicate_Opred_OPred @ ( hAPP @ ( c_Predicate_Oeval @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Oorder @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ C ) @ A )
| ~ ( c_Orderings_Oorder @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Odual__order_0) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Oorder @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ C ) @ A )
| ~ ( c_Orderings_Oorder @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(496,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Omono @ B @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Ostrict__mono @ E @ C @ A ) @ D ) )
| ~ ( c_Orderings_Oorder @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Ostrict__mono__mono_0) ).
thf(1930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Omono @ B @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Ostrict__mono @ E @ C @ A ) @ D ) )
| ~ ( c_Orderings_Oorder @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(676,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(2353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(630,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(2241,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)],[630]) ).
thf(320,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1532,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)],[320]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(258,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 ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(1384,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 ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(515,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( hAPP @ ( c_List_Onth @ B @ C ) @ A ) ) @ ( c_List_Oset @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__set__conv__nth_2) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( hAPP @ ( c_List_Onth @ B @ C ) @ A ) ) @ ( c_List_Oset @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(982,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)],[83]) ).
thf(91,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 ) @ D )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ A @ E ) @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ tc_bool ) @ B ) @ ( c_fequal @ E ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ B @ E ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__image__gen_0) ).
thf(1004,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 ) @ D )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ A @ E ) @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ tc_bool ) @ B ) @ ( c_fequal @ E ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ B @ E ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(236,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Oset @ B @ C ) )
= ( c_List_Ofoldl @ D @ E @ B @ C @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ D @ I @ J @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__set__fold_0) ).
thf(1331,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Oset @ B @ C ) )
= ( c_List_Ofoldl @ D @ E @ B @ C @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ D @ I @ J @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ( B = C )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_Oneq__le__trans_0) ).
thf(1962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ( B = C )
| ~ ( c_Orderings_Oorder @ D @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(384,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1681,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)],[384]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(712,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(2436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(570,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(2106,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)],[570]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1069,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LeastI__ex_0) ).
thf(2321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(502,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ B @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Omono @ E @ F @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ E @ G @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order_OmonoD_0) ).
thf(1944,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ B @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Oorder_Omono @ E @ F @ A ) @ B ) )
| ~ ( c_Orderings_Oorder @ E @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ~ ( class_Lattices_Oupper__semilattice @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ E ) ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__sup_0) ).
thf(940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ~ ( class_Lattices_Oupper__semilattice @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ E ) ) ) @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ E ) ) ) )
| ~ ( hBOOL @ ( c_Orderings_Oorder__class_Omono @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(58,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(923,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) )
= ( c_Nat_Osize__class_Osize @ E @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(614,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(2206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LeastI_0) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Owellorder @ A )
| ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(2059,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(1037,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)],[105]) ).
thf(713,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ ( c_Type_Otype_OFun @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(2438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ c_Type_Otyping @ A ) @ B ) @ ( c_Type_Otype_OFun @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(2238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_0) ).
thf(2170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(675,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) ) @ D ) )
| ~ ( hBOOL @ ( c_Relation_Otrans @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(2351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ E ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Pair @ A @ A ) @ B ) @ E ) ) @ D ) )
| ~ ( hBOOL @ ( c_Relation_Otrans @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(608,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I4_J_0) ).
thf(2191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(444,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(1812,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(882,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)],[39]) ).
thf(601,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(2177,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)],[601]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(1014,plain,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I2_J_1) ).
thf(1417,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) ) @ E ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(471,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(2640,plain,
$false,
inference(e,[status(thm)],[1337,2094,1024,1369,2306,1633,1995,1729,1031,1899,893,2559,2331,1956,2199,1322,1586,1501,2452,809,2109,1454,2031,1559,1105,1237,846,1315,1850,1083,962,1818,1295,1158,2117,2231,2395,1618,994,1401,1073,1205,2114,2380,1793,1692,1305,1041,1200,2077,1924,2210,1443,1808,1569,1939,1705,1608,1137,2607,1310,2184,2448,2141,1872,1988,913,945,1954,1078,1788,1426,2476,2168,1260,1640,2580,1354,2146,930,2360,1095,1196,898,2046,2548,1441,841,1613,2010,1359,1601,2082,2516,1529,2405,1887,2227,1576,973,885,1650,1645,2173,1366,1904,1518,1703,1228,1482,1254,1287,2328,1430,2039,838,1826,1313,2562,1992,2126,1059,2571,1760,1298,1907,2501,1264,2217,1511,2274,917,1832,934,1545,853,2158,2024,1773,2388,1100,1922,817,902,1087,1514,2049,2552,969,2373,1741,1398,1115,2635,2301,1815,1494,1450,1109,2259,2451,1334,1978,2555,966,1489,1415,2616,1946,1302,1664,1714,2027,1682,834,1864,2122,2291,1020,2254,1183,2073,1051,821,1843,1169,1377,1215,2483,866,2530,2371,1394,1351,1433,2618,2281,1896,877,1526,2137,988,2286,2639,2103,1405,1104,1242,849,2392,2154,1696,2586,1651,942,2204,2473,1438,1470,1783,2296,2364,2164,1067,1736,2496,1768,1868,2382,2061,1636,1047,1057,1163,957,1091,2428,825,2249,2541,1580,1255,862,1676,1217,1751,1487,1824,815,2132,2528,2015,2264,2409,1387,1723,1423,2445,847,1920,2433,1968,1555,1178,1951,1687,1624,1836,1656,1407,1392,1910,1012,2609,830,2344,2313,1128,2492,2112,1291,1936,1592,1983,1762,1270,1804,1328,1064,1970,980,1540,1878,869,1755,2268,1397,1234,1541,1089,2498,874,1143,2377,948,1534,1017,2460,1361,1659,2323,2455,2080,2196,2349,1889,1039,1155,884,1329,1739,1461,901,1075,1810,1791,2551,1207,2085,997,985,2487,1131,1974,2465,911,1799,1874,1429,1720,1324,2504,1150,1478,1249,2519,1539,1456,1382,1266,1231,2355,1192,1932,1002,1852,2052,1599,1246,1857,1318,1202,938,2546,1779,2043,1563,1170,2440,2221,1026,926,2208,805,2057,1712,1054,1035,2368,1071,2402,2423,888,1278,1135,2001,1959,1219,1273,1747,1927,856,2602,2028,1374,2376,1631,2235,2144,1764,2413,2033,2149,1007,1916,1389,843,2525,2188,1752,1403,1965,1520,1124,1226,904,975,2225,1884,1795,1701,1139,2193,936,2326,1312,1865,1733,1107,2055,2166,1258,1707,2293,2308,1371,919,2557,1464,2474,1638,1224,2573,1356,2510,1209,2538,2151,1722,1771,1122,1690,1571,1194,2346,1282,2478,2415,1894,2637,1117,1574,1806,2284,2257,1589,2246,1603,880,1043,1801,863,1175,2182,1339,1557,2129,1731,799,1838,964,915,1344,2289,1293,1061,1820,1112,890,1667,2180,1080,2632,2593,1029,895,1022,2252,827,2481,1643,2139,2156,922,2069,2075,2418,1198,1841,1594,1699,2212,959,1445,2620,868,1775,2244,1435,2535,2101,1726,1364,2390,1496,2303,851,1102,2005,1626,1166,1467,2471,1420,2037,1684,2124,2629,1990,2597,823,2582,1049,1662,2614,2096,2318,2271,1145,2564,1547,2298,855,2397,1611,1743,887,971,1566,1647,2175,2407,1845,2513,2567,1605,2588,1941,954,1252,1484,2160,1499,2569,1716,1186,1262,2337,1901,1085,1679,2044,1336,2468,1300,1452,840,1785,2276,2219,951,2599,1934,2543,2579,1749,1504,1717,1881,2266,859,2411,2500,1543,1766,1141,2426,1981,1221,1284,2279,2357,1972,2320,1506,1585,978,1670,1797,1240,991,1617,2013,2458,2479,2088,1459,1180,931,1553,1949,1817,2310,2611,1781,1126,2071,1998,2626,1918,1834,1913,1654,1412,2215,1517,1448,2490,1189,1010,2342,1289,844,2443,1326,1476,1629,1745,2026,1854,2431,1523,2262,1276,2591,813,2594,1341,2098,1903,2135,2532,1508,1244,1822,1861,1491,2384,1777,2462,1308,2120,2315,2494,2623,1045,2399,2041,2576,2066,2362,2162,2183,1212,2230,2036,1161,1614,2421,2003,1348,999,1512,1280,1578,2385,1097,2233,1395,2522,1876,1480,2123,1133,1380,2604,2008,1986,1148,1673,867,1757,1859,1816,2334,2186,807,1693,1561,2366,2091,1891,1065,2340,2201,801,1172,1410,1033,1710,2223,960,1473,2021,1346,2063,1829,1268,1152,1582,2583,908,2507,2484,871,1621,1120,1093,1930,2353,1236,2241,1532,860,1384,1537,1976,1550,1597,982,1004,1331,1320,1962,1681,2018,2436,2106,1069,2321,1944,940,923,2206,1848,2059,1037,2438,2238,2170,2351,2191,1812,882,2177,1014,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL823-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n022.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % 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 16:28:48 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.86/1.10 % [INFO] Parsing done (248ms).
% 1.86/1.11 % [INFO] Running in sequential loop mode.
% 2.25/1.30 % [INFO] eprover registered as external prover.
% 2.25/1.30 % [INFO] cvc4 registered as external prover.
% 2.25/1.31 % [INFO] Scanning for conjecture ...
% 3.32/1.54 % [INFO] Found a conjecture and 797 axioms. Running axiom selection ...
% 3.82/1.74 % [INFO] Axiom selection finished. Selected 797 axioms (removed 0 axioms).
% 4.92/2.02 % [INFO] Problem is propositional (TPTP CNF).
% 4.92/2.04 % [INFO] Type checking passed.
% 4.92/2.04 % [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 ...
% 17.02/5.13 % External prover 'e' found a proof!
% 17.02/5.13 % [INFO] Killing All external provers ...
% 17.02/5.13 % Time passed: 4604ms (effective reasoning time: 4016ms)
% 17.02/5.13 % 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)>
% 17.02/5.13 % Axioms used in derivation (797): clsarity_nat__HOL_Oord, cls_Nil__is__map__conv_1, cls_the__sym__eq__trivial_0, cls_xt1_I9_J_0, cls_MI1_0, cls_linorder__antisym__conv2_1, cls_boolean__algebra_Ocompl__top__eq_0, cls_subst__lt_0, cls_UN__extend__simps_I3_J_1, cls_INFI__set__fold_0, cls_some__eq__trivial_0, cls_dB_Osimps_I6_J_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_inf__sup__absorb_0, cls_Int__Un__distrib_0, cls_order_Ole__less_0, clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_finite__Collect__disjI_1, cls_order_Oeq__iff_0, cls_bot__fun__eq_0, cls_apps__eq__Abs__conv_0, cls_UN__simps_I1_J_1, cls_order__le__less__trans_0, cls_sup__ge1_0, cls_image__constant_0, cls_INT__simps_I7_J_0, cls_lift_Osimps_I2_J_0, cls_insertE_0, cls_UN__simps_I3_J_1, cls_SUPR__def__raw_0, cls_in__listsp__conv__set_0, cls_order_Oantisym_0, cls_subst__App_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_insert__inter__insert_0, cls_boolean__algebra_Ocompl__sup__top_0, cls_boolean__algebra_Odiff__eq_0, cls_single__valuedD_0, cls_sup__top__left_0, cls_subst__eq_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_Image__def__raw_0, cls_dB_Osimps_I8_J_0, cls_LeastI_0, cls_INT__extend__simps_I9_J_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, clsarity_nat__Lattices_Odistrib__lattice, cls_update__accessor__congruence__foldE_0, cls_set__conv__nth_0, cls_finite__insert_0, cls_append__self__conv_0, cls_set__empty2_1, cls_Image__singleton__iff_0, cls_strict__mono__eq_0, cls_UN__extend__simps_I2_J_1, cls_subject__reduction_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Un__empty__left_0, cls_INT__extend__simps_I5_J_0, cls_Un__INT__distrib2_0, cls_set__empty_1, cls_INT__D_0, clsarity_bool__Lattices_Olower__semilattice, cls_distrib__sup__le_0, cls_le__SUPI_0, cls_linorder__neqE_0, cls_UN__extend__simps_I5_J_0, cls_strict__mono__less_0, cls_UN__extend__simps_I10_J_0, cls_update__accessor__noopE_0, cls_COMBK__def_0, cls_image__Int_0, cls_UnCI_1, cls_boolean__algebra_Ocompl__bot__eq_0, clsarity_Predicate__Opred__Lattices_Olattice, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_CHAINED_0, cls_inf__sup__aci_I6_J_0, cls_Un__commute_0, cls_eval_Osimps_0, cls_nth__mem_0, cls_listsp__infI_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_MI2_0, cls_pred__equals__eq2_0, cls_listsp__conj__eq_0, cls_Int__insert__left_0, cls_finite__Collect__disjI_0, cls_empty__iff_0, cls_app__Var__IT_0, cls_le__inf__iff_1, cls_boolean__algebra_Ocompl__inf__bot_0, cls_less__supI1_0, cls_Int__Un__distrib2_0, cls_mem__def_1, clsarity_Predicate__Opred__Orderings_Obot, cls_appR_0, clsarity_nat__Orderings_Olinorder, cls_Int__Collect_1, cls_uIT_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_Image__Un_0, cls_UN__simps_I2_J_1, cls_insert__iff_1, cls_COMBI__def__raw_0, cls_sup__inf__distrib2_0, cls_le__sup__iff_0, cls_inf__left__commute_0, cls_inj__on__Un__image__eq__iff_0, cls_listsp_ONil_0, cls_inf1E_1, cls_Collect__conj__eq_0, cls_Image__singleton_0, cls_LeastM__def_0, cls_eq__Nil__appendI_0, cls_Image__eq__UN_0, cls_inf__sup__distrib1_0, cls_order__less__trans_0, cls_self__append__conv_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_Eps__split__eq_0, cls_rtranclp__trans_0, cls_complete__lattice_OInf__set__fold_0, cls_same__append__eq_0, clsarity_fun__Lattices_Oupper__semilattice, cls_adm__lemma_0, cls_splitI_0, cls_pred__equals__eq_0, cls_COMBB__def_0, cls_INT__absorb_0, cls_CollectI_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_INT__insert__distrib_0, cls_subst__preserves__beta_0, clsarity_fun__Orderings_Otop, cls_INF__leI_0, cls_finite__insert_1, cls_finite__Collect__bex_0, cls_lift__type_0, cls_inf__commute_0, cls_rtranclp__r__diff__Id_0, cls_UN__simps_I1_J_0, cls_dB_Osimps_I7_J_0, cls_inj__image__mem__iff_0, cls_UN__simps_I4_J_0, cls_Nil__is__map__conv_0, cls_mult__less__cancel__right__disj_3, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_length__map_0, cls_INFI__def__raw_0, cls_Image__Collect__split_0, clsarity_bool__HOL_Oord, cls_cut__apply_0, cls_nat__less__cases_0, cls_INT__simps_I6_J_0, cls_finite__Int_1, cls_Collect__empty__eq_0, cls_sup__Inf1__distrib_0, cls_le__supI_0, cls_INT__empty_0, cls_UN__extend__simps_I1_J_0, cls_Inf__binary_0, cls_CollectD_0, cls_COMBS__def_0, cls_finite__Collect__bounded__ex_1, clsarity_nat__Ring__and__Field_Osemiring__0, cls_inf__Sup1__distrib_0, cls_Un__Int__distrib2_0, cls_append__eq__append__conv2_4, cls_inf2E_0, cls_Var__apps__eq__Var__apps__conv_0, cls_Int__empty__right_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_UN__singleton_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_order__less__asym_0, cls_inf__fun__eq_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_eval__inject_0, cls_order_Oneq__le__trans_0, cls_empty__is__image_0, cls_filter__append_0, cls_iso__tuple__update__accessor__cong__assist__id_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_Int__UN__distrib_0, cls_order_Ostrict__monoD_0, cls_rev__image__eqI_0, clsarity_Predicate__Opred__Orderings_Opreorder, cls_INT__constant_0, cls_class__semiring_Omul__c_0, cls_le__supE_1, cls_UN__iff_2, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_finite__image__set_0, cls_SUP__const_0, cls_complete__lattice_OSup__set__fold_0, cls_shift__eq_0, cls_linorder__antisym__conv1_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_Image__empty_0, cls_in__set__conv__nth_2, cls_range__composition_0, cls_SUP1__I_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_linorder__antisym__conv2_0, cls_The__split__eq_0, cls_UN__simps_I3_J_0, cls_le__iff__sup_0, cls_Sup__UNIV_0, cls_dB_Osimps_I3_J_0, cls_complete__lattice_OSup__Inf_0, cls_cuts__eq_0, cls_nth__map_0, cls_setsum__product_0, cls_linorder__neqE__nat_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_UN__insert__distrib_0, cls_image__id_0, cls_image__constant__conv_1, cls_THE__default__def__raw_0, cls_Un__UNIV__right_0, cls_SigmaI_0, cls_single__valued__def__raw_0, cls_finite__Int_0, cls_id__apply_0, cls_rel__comp__def__raw_0, cls_some__sym__eq__trivial_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_subst__Var_2, cls_filter_Osimps_I1_J_0, cls_inf__sup__aci_I8_J_0, cls_less__le__not__le_2, cls_order_OmonoD_0, cls_xt1_I10_J_0, cls_Nil__is__append__conv_0, cls_set__map_0, cls_dual__order_0, cls_Int__insert__right_1, cls_inf__top__right_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_inf__Sup__absorb_0, cls_sup__eq__bot__eq2_0, cls_image__def__raw_0, cls_in__listsp__conv__set_1, cls_UN__extend__simps_I9_J_0, cls_distrib__lattice_Oinf__sup__distrib1_0, cls_append__Nil2_0, cls_ord_OLeast__def__raw_0, cls_order_Ostrict__mono__def__raw_0, cls_UnCI_0, cls_not__less__iff__gr__or__eq_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__Least_0, cls_append__self__conv2_0, cls_UN__Un_0, cls_boolean__algebra_Odouble__compl_0, cls_filter__empty__conv_0, cls_singleton__iff_1, cls_SUPR__set__fold_0, cls_Powp__def_0, cls_INT__extend__simps_I10_J_0, cls_Collect__mem__eq_0, clsarity_fun__HOL_Oord, cls_single__valued__rel__comp_0, cls_pred_Oinject_0, cls_type_Osimps_I2_J_1, cls_inf__eq__top__eq1_0, cls_UN__simps_I10_J_0, cls_ATP__Linkup_OCOMBC__def_0, cls_self__append__conv2_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_insert__code_2, cls_CHAINED_0_01, cls_lists__typings_0, cls_self__append__conv2_1, cls_inf2I_0, cls_dB_Osimps_I4_J_0, cls_Inf__fin__Inf_0, cls_complete__lattice_OInf__UNIV_0, cls_image__insert_0, cls_typing__elims_I1_J_0, cls_length__filter__less_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_append__Nil_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_bind__def_0, cls_append__eq__append__conv2_5, cls_order_Ole__neq__trans_0, cls_append__in__listsp__conv_1, cls_set__empty2_0, cls_append__is__Nil__conv_2, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_map__is__Nil__conv_0, 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% 17.02/5.13 % No. of inferences in proof: 1597
% 17.02/5.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4604 ms resp. 4016 ms w/o parsing
% 17.82/5.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.82/5.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------