TSTP Solution File: LCL776-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL776-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:36 EDT 2023
% Result : Unsatisfiable 16.15s 4.45s
% Output : Refutation 16.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 971
% Syntax : Number of formulae : 1843 ( 477 unt; 100 typ; 0 def)
% Number of atoms : 4405 (1258 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 27366 (2380 ~;2662 |; 0 &;22324 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 158 ( 158 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 100 usr; 12 con; 0-5 aty)
% Number of variables : 4682 ( 0 ^;4682 !; 0 ?;4682 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(v_s_type,type,
v_s: $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(v_ss_type,type,
v_ss: $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(v_i_type,type,
v_i: $i ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(c_List_Orev_type,type,
c_List_Orev: $i > $i > $i ).
thf(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
thf(c_List_Otake_type,type,
c_List_Otake: $i > $i > $i > $i ).
thf(c_List_Otl_type,type,
c_List_Otl: $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(c_List_Olist__update_type,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_List_Orotate1_type,type,
c_List_Orotate1: $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_List_Obutlast_type,type,
c_List_Obutlast: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_List_Onth_type,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(c_HOL_Osgn__class_Osgn_type,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(c_Transitive__Closure_Ortranclp_type,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Osgn__if_type,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_List_Osko__List__XCons__eq__append__conv__1__1_type,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
thf(c_ListOrder_Ostep1_type,type,
c_ListOrder_Ostep1: $i > $i > $i ).
thf(c_List_Osko__List__Xappend__eq__Cons__conv__1__1_type,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Ohd_type,type,
c_List_Ohd: $i > $i > $i ).
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_List_Olast_type,type,
c_List_Olast: $i > $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_type,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(c_Ring__and__Field_Oordered__semidom__axioms_type,type,
c_Ring__and__Field_Oordered__semidom__axioms: $i > $i > $i > $i > $o ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_type,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(20,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(892,plain,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(1718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(2094,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(829,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(2778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2072,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(1995,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(676,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(2412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(21,axiom,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(893,plain,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(737,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(2559,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_List_Oappend @ A @ C @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(2331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(481,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(1956,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(618,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(2280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(581,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(2199,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(1322,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ F @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(849,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 ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(2822,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 ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(767,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(2630,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ E @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist__update @ B @ D @ E @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(759,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(2612,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
= ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(629,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(2306,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(644,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(2341,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(554,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(2131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(267,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(1454,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)],[267]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(2595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(712,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 ) ) ) )
| ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_1) ).
thf(2499,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 ) ) ) )
| ( ( c_List_Olist__update @ B @ A @ ( c_List_Onth @ B @ A @ C ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(2480,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(655,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(2363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(390,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) ) @ ( c_List_Olist_OCons @ A @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(1750,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ C @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) ) @ ( c_List_Olist_OCons @ A @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(710,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(2495,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(524,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Oappend @ ( c_List_Otake @ B @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__take__nth__drop_0) ).
thf(2062,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Oappend @ ( c_List_Otake @ B @ A @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(334,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(1618,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)],[334]) ).
thf(750,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(2590,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ C ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ A @ B ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lists__accD_0) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ C ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ A @ B ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ v_r @ v_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(873,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ v_r @ v_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(619,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2282,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(137,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(1142,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)],[137]) ).
thf(204,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1305,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(1437,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(149,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(1173,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(630,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(2309,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)],[630]) ).
thf(717,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(2512,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)],[717]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(2117,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(246,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1406,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
!= ( c_List_Orev @ C @ B ) )
| ( C
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(828,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(2776,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1808,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(1544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(504,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(2014,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(6,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(878,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(2380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(487,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_1) ).
thf(1971,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(407,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
thf(1793,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Odiv @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(863,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(2854,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__less_1) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(206,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(1310,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(513,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(2035,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)],[513]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(2448,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A
= ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_0) ).
thf(1275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A
= ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(1233,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_Suc @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(2042,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(757,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(2607,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(790,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(2686,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(1867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otake @ B @ C @ D ) @ D )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ ( c_List_Odrop @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__1__Cons_0) ).
thf(2184,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(633,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(2316,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(685,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(2434,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(442,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(1872,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)],[442]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(2459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ D @ B ) )
| ( A
= ( c_List_Oappend @ ( c_List_Orev @ D @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(480,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(1954,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)],[480]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1507,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olast @ A @ D ) )
| ( B
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_1) ).
thf(2360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olast @ A @ D ) )
| ( B
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__replicate_0) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(26,axiom,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(898,plain,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(426,axiom,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(1835,plain,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(13,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(885,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(1935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(1650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(2082,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(2173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(719,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(2516,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Odrop @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
thf(1803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(673,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
thf(2405,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(870,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(2869,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(1887,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(648,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(2348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= ( c_List_Olist_ONil @ D ) )
| ( A
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(806,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(2723,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(2432,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(240,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1391,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(380,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ E @ F ) @ ( c_List_Olist_OCons @ B @ D @ F ) ) @ ( c_List_Olist_OCons @ A @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(1724,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ E @ F ) @ ( c_List_Olist_OCons @ B @ D @ F ) ) @ ( c_List_Olist_OCons @ A @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(1475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(671,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(2400,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)],[671]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(1967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(556,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(2136,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)],[556]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(370,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(1703,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)],[370]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(811,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(2735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(2339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oreplicate @ B @ C @ D ) @ D )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(612,axiom,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
thf(2269,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(820,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
thf(2755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(800,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(2708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(421,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1826,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(208,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(1313,plain,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(798,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
thf(2703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(1760,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(1660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(589,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2217,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1511,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(615,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(2274,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(934,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_5) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(52,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(949,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(742,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).
thf(2571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(651,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2356,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(1800,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(802,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(2713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
!= ( c_Power_Opower__class_Opower @ D @ ( c_Suc @ C ) @ A ) )
| ( B = D )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(179,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1247,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__greater_0) ).
thf(2767,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(660,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(2373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(809,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(2730,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)],[809]) ).
thf(344,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(1641,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(862,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(2852,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)],[862]) ).
thf(726,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(2533,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)],[726]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(852,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(2829,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(792,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(2691,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(30,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(902,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(2403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(1514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1890,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A ) @ A )
= ( c_List_Ohd @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(9,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(881,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(769,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(2635,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__take_0) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1568,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ A @ D @ C ) )
| ~ ( 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(2301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ A @ D @ C ) )
| ~ ( 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)],[627]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Oappend @ C @ D @ B ) ) @ ( c_List_Oappend @ C @ E @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(1815,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Oappend @ C @ D @ B ) ) @ ( c_List_Oappend @ C @ E @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(694,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(2456,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(42,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(924,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C ) )
| ( ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_1) ).
thf(1450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C ) )
| ( ( c_Int_Onumber__class_Onumber__of @ D @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(1109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(775,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(2650,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(2236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(140,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(1151,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)],[140]) ).
thf(320,axiom,
! [D: $i,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 ) ) ) )
| ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_0) ).
thf(1581,plain,
! [D: $i,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 ) ) ) )
| ( ( c_List_Onth @ ( c_List_Olist__update @ B @ A @ D @ C ) @ A @ C )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(33,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(905,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(354,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(1664,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)],[354]) ).
thf(836,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(2794,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(637,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
thf(2324,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(623,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(2291,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)],[623]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(2254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
| ~ ( c_lessequals @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__take_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
| ~ ( c_lessequals @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(854,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(2833,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(449,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1886,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(1526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(2809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) )
| ( A
= ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(1943,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(841,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(2804,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(667,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(2392,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(2718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(748,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(2586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_1) ).
thf(1843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C ) )
| ( D
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(523,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(2058,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(2367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(468,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1928,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(2530,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(125,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(1119,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)],[125]) ).
thf(659,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(2371,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)],[659]) ).
thf(839,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olist__update @ ( c_List_Orev @ A @ D ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__update_0) ).
thf(2799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olist__update @ ( c_List_Orev @ A @ D ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ B @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(771,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
= D )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(2639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C )
= D )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).
thf(2011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(1206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(942,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ F @ D )
= ( c_List_Olist__update @ ( c_List_Olist__update @ A @ E @ F @ D ) @ B @ C @ D ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(583,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ B ) ) @ ( c_List_Olist_OCons @ C @ E @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(2204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ C @ D @ B ) ) @ ( c_List_Olist_OCons @ C @ E @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(743,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(2574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(812,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(2737,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(2296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1199,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(567,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(2164,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(537,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(2093,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
= D )
| ( ( c_List_Olist_OCons @ A @ B @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_2) ).
thf(1736,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
= D )
| ( ( c_List_Olist_OCons @ A @ B @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(763,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(780,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(2660,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)],[780]) ).
thf(397,axiom,
! [A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_expand__Suc_0) ).
thf(1768,plain,
! [A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(663,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(2382,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(827,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(2773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(499,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(2000,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(98,axiom,
class_OrderedGroup_Osemigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).
thf(1057,plain,
class_OrderedGroup_Osemigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(610,axiom,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I1_J_0) ).
thf(2264,plain,
! [A: $i] :
( ( c_List_Otl @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(1387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).
thf(2249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(287,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(1502,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(420,axiom,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_0) ).
thf(1824,plain,
! [A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(2032,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(677,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ A @ ( c_List_Olist__update @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ E @ C ) @ C ) )
| ( 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_list__update__append_1) ).
thf(2414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ A @ ( c_List_Olist__update @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ E @ C ) @ C ) )
| ( 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)],[677]) ).
thf(724,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(669,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
= ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(2396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ E @ D )
= ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(2441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(785,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(2673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__tl_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Odrop @ A @ B @ D ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(22,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(894,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(729,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2541,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1676,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(555,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(175,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
| ~ ( 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_list__update__append_0) ).
thf(1238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
| ~ ( 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)],[175]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(690,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( D = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ E @ C @ B ) ) @ ( c_List_Olist_OCons @ F @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(2445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( D = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ E @ C @ B ) ) @ ( c_List_Olist_OCons @ F @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(821,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2758,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(703,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
thf(2477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(7,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(879,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(151,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(1178,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)],[151]) ).
thf(871,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(2872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(200,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1296,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(1687,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) @ E @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2068,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(758,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( B = E )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(2609,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( B = E )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(17,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(889,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(814,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(2741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(1910,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_1) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(427,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(1837,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(766,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 ) @ ( c_Suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(2628,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 ) @ ( c_Suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(2670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(781,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(2663,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(638,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(2327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__1__Cons_0) ).
thf(2211,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(2492,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(732,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(2547,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C )
= ( c_List_Odrop @ B @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__drop_H_0) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ A @ B @ C ) @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ C ) @ C )
= ( c_List_Odrop @ B @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(595,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(2228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ C ) )
| ( 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_1) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ tc_nat ) @ C ) )
| ( 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)],[545]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__hd__tl_0) ).
thf(1291,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= ( c_List_Oappend @ ( c_List_Otl @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(825,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_H_6) ).
thf(2769,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(1012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ A @ B @ C @ D ) @ ( tc_List_Olist @ D ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(777,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(2653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(1106,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(324,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
| ~ ( 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_list__update__append1_0) ).
thf(1592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ A @ B @ C ) @ D @ E @ C )
= ( c_List_Oappend @ ( c_List_Olist__update @ A @ D @ E @ C ) @ B @ C ) )
| ~ ( 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)],[324]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_ONil @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_ONil @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oreplicate @ B @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oreplicate @ B @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__append__length_0) ).
thf(1328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ D )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(445,axiom,
! [A: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(1878,plain,
! [A: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(1755,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(770,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2638,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(70,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(989,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(602,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2245,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(224,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(1350,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)],[224]) ).
thf(2,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ v_r @ v_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(874,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ v_r @ v_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ v_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(857,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Ohd @ A @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(2840,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Ohd @ A @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(546,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(2115,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)],[546]) ).
thf(395,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(1762,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)],[395]) ).
thf(540,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(2100,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(2377,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(51,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(948,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ A @ B )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__conv__take_0) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ A @ B )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ ( c_List_Oappend @ B @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(12,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(884,plain,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(228,axiom,
! [C: $i,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 ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(1361,plain,
! [C: $i,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 ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(738,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__div__geq_0) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
thf(1739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Divides_Odiv__class_Odiv @ B @ C @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(321,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(1584,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)],[321]) ).
thf(473,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(1937,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)],[473]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(1810,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less__dividend_0) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(2317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(108,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(1082,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(29,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(901,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(679,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ B @ C ) @ ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc_0) ).
thf(2419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ ( c_List_Ohd @ B @ C ) @ ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(254,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1424,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(631,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(2312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(2053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(580,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(2196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(2551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(2472,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(92,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1039,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(970,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(831,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(2781,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)],[831]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(628,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 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(2304,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 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(1456,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(132,axiom,
class_Ring__and__Field_Osgn__if @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osgn__if) ).
thf(1131,plain,
class_Ring__and__Field_Osgn__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
thf(2243,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2566,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(477,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(1947,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(1715,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(1720,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(614,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(558,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(2140,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)],[558]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(621,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(2285,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)],[621]) ).
thf(122,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
thf(1114,plain,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(692,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(2450,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(2125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(2536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(201,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(1297,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)],[201]) ).
thf(788,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(2681,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(707,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(859,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(2845,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)],[859]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons_H_1) ).
thf(2153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_ONil @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(2387,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_ONil @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
thf(1668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(746,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2581,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(2465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
thf(984,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__tl_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Otl @ B @ C ) @ C )
= ( c_List_Otl @ ( c_List_Otake @ ( c_Suc @ A ) @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(714,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(2505,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(2006,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(2497,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(845,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono2_0) ).
thf(2813,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(256,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(1429,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(866,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(2862,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(705,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(2482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(795,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(2697,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(1991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(1779,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(2208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(41,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(921,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(530,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(2076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( A
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ D @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(1466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(591,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(453,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ E @ F ) @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(1895,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ E @ F ) @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) ) @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ D @ ( c_List_Olist_ONil @ F ) @ F ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(773,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(2645,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(761,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(2617,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(16,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(888,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(1732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(926,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(817,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(2749,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( ( c_List_Oappend @ C @ D @ B )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(1434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ tc_nat )
| ( ( c_List_Oappend @ C @ D @ B )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl_Osimps_I2_J_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(797,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2702,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(822,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Olast @ A @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(2761,plain,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ A @ B ) @ B )
= ( c_List_Olast @ A @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( 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(1846,plain,
! [C: $i,B: $i,A: $i] :
( ( ( 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)],[431]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(674,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(2408,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ A @ B ) @ C @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Suc @ C ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__nth_0) ).
thf(2089,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ A @ B ) @ C @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Suc @ C ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
thf(1278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(138,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(1146,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)],[138]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(2602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(2524,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(340,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(1631,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)],[340]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(2121,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(34,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(906,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(381,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(1727,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)],[381]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(1698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(1959,plain,
! [B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(2556,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Ohd @ A @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1548,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(467,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1927,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__mono_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ ( c_Divides_Odiv__class_Odiv @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(325,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(1595,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)],[325]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__less_0) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(32,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(904,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(462,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(1916,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(2188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(718,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(2514,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(3,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(875,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(803,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(2716,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(851,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Oappend @ C @ E @ B ) ) @ ( c_List_Oappend @ D @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(2827,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Oappend @ C @ E @ B ) ) @ ( c_List_Oappend @ D @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(2048,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(865,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(2859,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)],[865]) ).
thf(593,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(2225,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(448,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
thf(1884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(333,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(1615,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)],[333]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(834,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(2789,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(128,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(1125,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(779,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(2657,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(861,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(2849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) )
| ~ ( c_lessequals @ D @ C @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ tc_nat ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) )
| ~ ( c_lessequals @ D @ C @ tc_nat )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(708,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(2489,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(1652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
thf(1929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(1795,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(369,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(1701,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(670,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(2161,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(136,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(1139,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(1786,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(207,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(1312,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(498,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1997,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(1332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(819,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 ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2753,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 ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(2706,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
thf(2425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(113,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
= ( c_List_Onth @ A @ E @ D ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).
thf(1092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
= ( c_List_Onth @ A @ E @ D ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(561,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A
= ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_OCons @ D @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_2) ).
thf(2148,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A
= ( c_List_Olist_OCons @ D @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_OCons @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ A @ B ) @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lists__accI_0) ).
thf(2358,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ A @ B ) @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Obutlast @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__butlast_0) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Obutlast @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(1356,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(716,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2510,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(647,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
thf(2346,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orotate1 @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= ( c_List_Oappend @ B @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(2079,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(2521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(28,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(900,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(1542,plain,
! [B: $i,A: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(1722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(1771,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(8,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(880,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(1690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__append2_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Otl @ A @ C ) @ B @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(805,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2721,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(2119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
| ~ ( c_List_Olistsp @ A @ C @ D )
| ~ ( c_List_Olistsp @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(562,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_Ring__and__Field_Oordered__semidom__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oord__class_Oless @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ordered__semidom__class_Oaxioms_0) ).
thf(2151,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_Ring__and__Field_Oordered__semidom__axioms @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oord__class_Oless @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(772,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(533,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(2084,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(764,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(2624,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(680,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(2422,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(71,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(990,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(1933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(607,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(2257,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1589,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(603,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(2246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(1603,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(864,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(2856,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(840,axiom,
! [A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(2802,plain,
! [A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(850,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(2824,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(1339,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(632,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(2314,plain,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(496,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(1993,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(830,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(2780,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(1862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(915,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ C @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ C @ A @ B ) @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(617,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(2278,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(18,axiom,
class_Divides_Osemiring__div @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Divides_Osemiring__div) ).
thf(890,plain,
class_Divides_Osemiring__div @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(2180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(2025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(844,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2812,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(768,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(2632,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)],[768]) ).
thf(675,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).
thf(2410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_Suc @ D ) @ C )
= ( c_List_Onth @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1325,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(2593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(23,axiom,
class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(895,plain,
class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(730,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(2542,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Oappend @ E @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) @ ( c_List_Oappend @ F @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ D ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(2252,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(2329,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__drop_0) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Otl @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(479,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1952,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2710,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(1820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(1112,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(745,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(2578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(1171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(1841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ C @ D @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__acc__step1I_0) ).
thf(2365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ ( c_List_Olist_OCons @ C @ D @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( tc_List_Olist @ B ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(807,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(2725,plain,
! [B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ A @ B ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ A @ B ) @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(959,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Orev @ ( c_List_Orev @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(2835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(534,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(2086,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(11,axiom,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(883,plain,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(2369,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ A @ B @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(1176,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(838,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(2797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(541,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__take_0) ).
thf(2101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ A @ B @ C ) @ D @ C )
= ( c_List_Onth @ B @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(564,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__if_0) ).
thf(2156,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(793,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(2693,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Otake @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__butlast_0) ).
thf(1805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ ( c_List_Obutlast @ B @ C ) @ C )
= ( c_List_Otake @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(869,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
thf(2867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(1066,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Odrop @ A @ ( c_List_Obutlast @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1528,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(622,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(2288,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(1034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ E @ D )
= ( c_List_Olist__update @ A @ B @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(163,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1208,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(782,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ B @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_3) ).
thf(2665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( B
= ( c_List_Oappend @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ B @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(832,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(2784,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(776,axiom,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(2652,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(1905,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= B )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olist__update @ ( c_List_Obutlast @ A @ D ) @ B @ C @ D ) )
| ( B
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_1) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ B @ C @ D ) @ D )
= ( c_List_Olist__update @ ( c_List_Obutlast @ A @ D ) @ B @ C @ D ) )
| ( B
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(290,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(1509,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(939,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(275,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(1472,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(739,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(2564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( c_lessequals @ E @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
thf(2597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(1662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olistsp @ A @ B @ C )
| ~ ( c_List_Olistsp @ A @ ( c_List_Oappend @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(760,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(2614,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ D ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ D ) ) @ tc_nat ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(2107,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(789,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(2684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(2202,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
!= D )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( C
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
| ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
!= D )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B )
!= A )
| ( C
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) )
| ( ( c_List_Oappend @ C @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ A @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__div_0) ).
thf(1748,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(483,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(1961,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)],[483]) ).
thf(5,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ v_r ) ) @ v_s ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(872,plain,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ v_r ) ) @ v_s ) @ ( c_List_Oappend @ v_ss @ ( c_List_Olist_OCons @ ( c_Lambda_OdB_OVar @ v_i ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(1156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(15,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(887,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(848,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2821,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
= D )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_0) ).
thf(1230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Olist_OCons @ A @ ( c_List_Osko__List__XCons__eq__append__conv__1__1 @ A @ B @ D @ E @ C ) @ C )
= D )
| ( D
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(1798,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(2298,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(1516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(1598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(244,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(329,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(1605,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)],[329]) ).
thf(749,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(2588,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)],[749]) ).
thf(810,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ C @ D @ B ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(2732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) )
| ( ( c_List_Oappend @ A @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ C @ B ) @ D @ B ) @ B )
= ( c_List_Oappend @ C @ D @ B ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_Nat_Osize__class_Osize @ C @ ( tc_List_Olist @ B ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(55,axiom,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(954,plain,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(787,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons__number__of_1) ).
thf(2678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(720,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(2518,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)],[720]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__greater_1) ).
thf(2175,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
thf(1267,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(853,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(72,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(993,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(741,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(2569,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(536,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(2092,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ A @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__conv__nth_0) ).
thf(1790,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olast @ A @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(440,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(1869,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1235,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(642,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(2337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Otake @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
thf(1658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(517,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(2044,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1579,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(218,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(1336,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)],[218]) ).
thf(168,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ A @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__conv__nth_0) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ( ( c_List_Ohd @ A @ B )
= ( c_List_Onth @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(791,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( 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(2688,plain,
! [C: $i,B: $i,A: $i] :
( ( ( 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)],[791]) ).
thf(796,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
thf(2700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ A @ ( c_List_Obutlast @ B @ C ) @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
thf(2276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(490,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1980,plain,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(2128,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Oappend @ C @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(2545,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(2599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(856,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ C )
= ( c_List_Olist_OCons @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(2838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ C )
= ( c_List_Olist_OCons @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(288,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(1504,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)],[288]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ A @ B @ ( c_List_Onth @ A @ B @ C ) @ C )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ A @ B @ ( c_List_Onth @ A @ B @ C ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(786,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(2675,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)],[786]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(454,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(1898,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(225,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(1353,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)],[225]) ).
thf(652,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(2357,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)],[652]) ).
thf(858,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(2843,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= ( c_List_Oappend @ ( c_List_Otake @ B @ A @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ D ) @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
thf(2145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
= ( c_List_Oappend @ ( c_List_Otake @ B @ A @ D ) @ ( c_List_Olist_OCons @ C @ ( c_List_Odrop @ ( c_Suc @ B ) @ A @ D ) @ D ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(1485,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(808,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(2728,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(376,axiom,
class_Int_Onumber @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(1717,plain,
class_Int_Onumber @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(2030,plain,
! [B: $i,A: $i] :
( ( c_List_Otake @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(447,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1881,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(842,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(2807,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(611,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(2266,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(4,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(876,plain,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tl__replicate_0) ).
thf(1940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otl @ ( c_List_Oreplicate @ A @ B @ C ) @ C )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(686,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
= E )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(2435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ A @ C ) @ B @ C )
= E )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ D @ ( tc_List_Olist @ C ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(1839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(695,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(2458,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(2045,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(847,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
= B )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(2818,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ A @ B @ C )
= B )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(1685,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(1949,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(588,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(2215,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)],[588]) ).
thf(129,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1126,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(765,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(2626,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(1918,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_1) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(794,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(2696,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(976,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(31,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(903,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) )
| ( ( c_List_Onth @ A @ B @ D )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__same__conv_0) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist__update @ A @ B @ C @ D )
!= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) )
| ( ( c_List_Onth @ A @ B @ D )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(19,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(891,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2743,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(2342,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ A @ B @ C ) @ ( tc_List_Olist @ C ) ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(1289,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(2226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(266,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(1453,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)],[266]) ).
thf(384,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(1734,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(835,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) ) @ ( c_List_Olist_OCons @ C @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(2792,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ D ) @ ( c_List_Olist_OCons @ B @ E @ D ) ) @ ( c_List_Olist_OCons @ C @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(182,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(1253,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc_0) ).
thf(961,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Odrop @ A @ ( c_List_Otl @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(1639,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(735,axiom,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2554,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(1745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1854,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__length01_0) ).
thf(1523,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
= A )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(723,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(2526,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(668,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(2394,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(2443,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(568,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(2167,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(2283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(666,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(2389,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)],[666]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
= ( c_List_Onth @ A @ E @ D ) )
| ( B = E )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update_1) ).
thf(1341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ E @ D )
= ( c_List_Onth @ A @ E @ D ) )
| ( B = E )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(24,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(896,plain,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(823,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(2764,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)],[823]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(1822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ D ) @ A ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Suc @ D ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
thf(995,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(609,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(2262,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(744,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(2576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
| ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Cons__number__of_1) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Olist_OCons @ B @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ D ) @ D ) )
| ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1607,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(27,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(899,plain,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(94,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ D )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ B @ C @ D ) @ ( c_Int_Onumber__class_Onumber__of @ A @ tc_nat ) @ D )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
thf(2475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(833,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(2786,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)],[833]) ).
thf(774,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
thf(2648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(1777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(199,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(1294,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ A ) @ ( tc_List_Olist @ A ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(697,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(2462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
= ( c_List_Olist_ONil @ C ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(2230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(624,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
thf(2294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(813,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(2739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1774,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(597,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Onth @ B @ A @ C )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).
thf(2233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Onth @ B @ A @ C )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1546,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(756,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__drop_0) ).
thf(2604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Olast @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1757,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(278,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(1480,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)],[278]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ D )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__list__update__eq_0) ).
thf(2003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ A @ B @ C @ D ) @ B @ D )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(2218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(2385,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ A @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Orev @ B @ C ) @ ( c_List_Orev @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1678,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__rotate1_0) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orotate1 @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(242,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(1395,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)],[242]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(846,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(2815,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(493,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(1986,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(502,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(2008,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(1303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(180,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(1248,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)],[180]) ).
thf(520,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2050,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Suc @ B ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(436,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(1859,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(818,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(2751,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(918,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(641,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(2334,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(576,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(2186,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(816,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
= E )
| ( B
= ( c_List_Olist_OCons @ D @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_3) ).
thf(2746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
= E )
| ( B
= ( c_List_Olist_OCons @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(762,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ E @ C @ B ) ) @ ( c_List_Olist_OCons @ F @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(2619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ A @ B ) @ ( c_List_Olist_OCons @ E @ C @ B ) ) @ ( c_List_Olist_OCons @ F @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(2040,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(783,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(2668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ ( c_Suc @ A ) @ ( c_List_Olist_OCons @ B @ C @ D ) @ D )
= ( c_List_Odrop @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(1363,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(209,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(1314,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)],[209]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(1693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(2070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(25,axiom,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(897,plain,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ D @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(678,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(2417,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(2223,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(837,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(2795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(507,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(2021,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)],[507]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1610,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(14,axiom,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(886,plain,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(387,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(1742,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(733,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(2549,plain,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(650,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(2353,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)],[650]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(2159,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ A ) @ B @ C @ A )
= ( c_List_Olist_ONil @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_length__tl_0) ).
thf(1827,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(2430,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(235,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1378,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(699,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
= E )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_1) ).
thf(2467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( ( c_List_Oappend @ ( c_List_Osko__List__Xappend__eq__Cons__conv__1__1 @ D @ E @ A @ B @ C ) @ B @ C )
= E )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Orev @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(1550,plain,
! [B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Orev @ B @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate1__is__Nil__conv_0) ).
thf(2507,plain,
! [B: $i,A: $i] :
( ( ( c_List_Orotate1 @ A @ B )
!= ( c_List_Olist_ONil @ B ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( 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(1925,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(456,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1902,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(613,axiom,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ A @ ( c_List_Olist_ONil @ B ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(713,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
thf(2502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(2241,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(552,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__le__dividend_0) ).
thf(2127,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Odiv @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_HOL_Osgn__class_Osgn @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(860,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(2847,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(237,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(1384,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)],[237]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(2485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(301,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1537,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(728,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(2539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(867,axiom,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(2864,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(446,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1880,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(2321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(476,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(1945,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)],[476]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(2206,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ A @ B ) @ ( c_List_Olist_OCons @ C @ ( c_List_Olist_ONil @ B ) @ B ) @ B ) @ B )
= ( c_List_Olist_OCons @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(251,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(693,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(2453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(1912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(153,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(1184,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(529,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(2074,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ( ( c_List_Olast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_last__list__update_0) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Olist_ONil @ B ) )
| ( ( c_List_Olast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Onth @ B @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hd__drop__conv__nth_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ A @ B @ C ) @ C )
= ( c_List_Onth @ B @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(506,axiom,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I2_J_1) ).
thf(2018,plain,
! [B: $i,A: $i] :
( ( ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ ( c_List_Otl @ A @ B ) @ ( tc_List_Olist @ B ) ) ) )
| ( A
= ( c_List_Olist_ONil @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(868,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2866,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_take__Suc__conv__app__nth_0) ).
thf(2438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Otake @ ( c_Suc @ A ) @ B @ C )
= ( c_List_Oappend @ ( c_List_Otake @ A @ B @ C ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ B @ A @ C ) @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(599,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(2238,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(2170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_butlast__list__update_0) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Obutlast @ ( c_List_Olist__update @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ A @ ( tc_List_Olist @ B ) ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ C @ B ) @ B )
= ( c_List_Obutlast @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(578,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(2191,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(415,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(1812,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)],[415]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(700,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(2470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(10,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(882,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Odrop @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Orev @ ( c_List_Otake @ A @ B @ C ) @ C )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ B @ ( tc_List_Olist @ C ) ) @ A @ tc_nat ) @ ( c_List_Orev @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Orev @ A @ B )
!= ( c_List_Orev @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(826,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(2771,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)],[826]) ).
thf(2892,plain,
$false,
inference(cvc4,[status(thm)],[892,1586,1718,2094,2778,2072,1995,1559,2412,909,1899,893,2559,2331,1956,2280,2199,1322,1036,2822,2630,2612,1024,1168,2306,2341,2131,1454,2595,2499,2427,2480,2363,1750,1068,2495,2062,1618,2590,1422,873,2282,1142,1305,1437,1173,1158,2309,2512,2117,1406,2104,2776,1808,1544,2014,878,2380,1971,1793,2854,1497,1788,1671,1655,1137,1310,2035,2448,1275,1233,1260,913,945,2042,1458,2607,2686,1867,2184,1164,2316,2434,1872,1988,2459,1063,1954,1507,2360,1095,1196,898,1835,885,1935,1650,1601,2082,2173,2516,1803,2405,2869,1887,2348,2723,2432,1914,1243,1127,1391,1576,1724,1475,2400,1967,2136,1518,1265,1703,1228,1623,1482,1287,1709,1430,2735,2339,2269,2755,2708,1826,1313,1132,2703,1760,1660,1330,2217,1511,2274,934,1191,949,2571,2356,1800,2713,1892,1247,2767,2373,2730,1641,2852,2533,1100,2829,1922,2691,902,2403,1514,1319,1890,1398,881,1115,2635,1931,1568,2301,1815,2456,924,1450,1373,1109,2650,2236,1334,1151,1581,905,1664,2794,2324,2027,2291,2254,981,2833,1215,1447,1886,1526,2809,1943,2804,1104,2392,2718,2586,1843,2058,2367,1928,1072,2530,1119,2371,2799,2639,2011,1206,942,2204,2574,2737,2296,1199,2164,1470,2093,1736,2621,2660,1768,2382,2773,2000,1730,1057,2264,1387,2249,1255,1123,1502,1666,1824,2032,2414,2528,2396,2441,2673,957,1223,894,1042,952,2541,1676,2133,1238,2015,2445,2758,1920,2477,879,1178,2872,1296,1687,2068,2609,889,2741,1910,1573,1032,1837,1365,2628,2670,2663,1555,1079,1027,2327,2213,2211,1407,2492,2547,2344,1392,2228,2112,1291,2769,1012,2653,1106,1592,1983,1270,1534,1328,1878,1755,2638,989,2245,1350,874,2840,2115,1762,2100,2377,948,1375,1121,1540,1006,1683,884,1361,1964,2561,1739,1584,1937,1810,2038,2317,1082,2023,901,2419,1075,1424,2312,1414,2053,2196,2551,1016,1612,2472,1039,970,2781,1419,1478,2304,1456,1131,2243,2566,1947,1874,1715,1720,2272,2140,1627,2285,1114,1263,997,2450,2125,2536,1297,2681,2487,2845,2153,2387,1831,1668,1974,2581,2465,984,911,2505,2006,2497,1002,1852,2813,1429,2862,2482,2697,1991,1202,1086,1779,2208,1695,921,1563,2076,1466,2221,1895,2645,2617,888,1732,926,2749,1434,1857,1241,2702,2761,1846,1054,2408,2089,1278,1648,1251,1146,1273,2602,2524,1631,2260,2121,906,965,1727,1698,1959,2556,1548,1927,1301,1595,1154,904,1833,1916,2188,2514,875,1403,2716,1520,1488,2827,2048,2859,2225,1884,1615,1784,1389,2789,1125,2657,2849,1620,2489,1652,1929,1795,1701,2398,2161,1139,1786,936,1371,1312,1865,1635,1058,1997,1332,2753,2706,1090,2425,1258,2055,1092,2148,2358,2319,1356,2510,2346,2079,2521,900,1282,2097,1542,1722,1771,880,1690,1571,1969,2065,1209,2721,2119,2151,2642,2084,2624,2422,1117,990,1933,2257,1589,2246,1492,1603,2856,2802,2824,2182,1339,1557,2314,1993,2780,1862,915,1344,2278,1381,890,2180,2025,2812,2632,2410,1325,2593,1029,895,2542,1460,1022,2252,2329,932,1061,1952,2710,1820,1112,2578,1171,1841,2365,2725,959,2835,1245,2086,1643,883,2369,1176,2797,1000,2101,1102,2156,2693,1805,2867,1066,1445,1528,986,2288,1034,1208,2665,2784,2652,1905,1134,1509,939,1472,2564,2597,1049,1662,2614,1166,2107,2684,2202,968,1181,1748,1961,872,1156,887,2143,2821,1230,1798,2298,1516,1598,1225,1400,1605,2588,2732,954,2678,2518,1368,2175,1753,1267,2831,993,2569,2092,1790,1432,1869,1235,2337,1658,2044,1579,1336,1220,907,1711,1499,1637,2688,2700,1186,2276,1980,2128,2545,2599,1285,1218,1766,2838,1981,1427,1504,978,1008,2584,2675,1358,1898,1849,1353,2357,2843,2145,1485,1052,2728,1717,2030,1881,2807,2266,876,1940,2435,1839,2458,2045,2818,1685,1949,1817,2194,1412,2215,1126,2626,1918,1316,1084,2696,1553,976,903,1781,891,2743,1189,2110,1010,2342,1289,2226,1453,1734,2792,1253,961,1639,2554,1629,1745,1854,1523,2526,2394,1646,2443,963,2167,2283,2389,1341,896,2764,1822,995,2262,1440,1308,2576,1077,1212,1607,899,1045,1161,2475,2786,2648,1777,1294,2462,1706,1193,2230,2294,2739,1442,1348,1774,1280,2233,1546,2604,1876,1757,1480,1908,2003,2123,2218,2385,1678,950,1097,1395,1625,2815,1986,2008,1303,1148,1673,1248,2050,1859,2751,918,1495,2334,2186,2746,1561,2619,2040,2668,955,1363,1314,1693,2070,897,1410,2417,2223,2795,2021,1346,1610,886,1742,2549,928,2353,2159,1827,2430,1378,1019,2467,1550,2507,1925,1902,2270,2138,2502,2241,2127,1829,1977,1129,1532,2847,1384,2485,1537,2539,1713,2864,1880,1004,2321,1945,2206,1416,2453,1912,1681,1184,2074,1463,1565,2018,2866,1490,2438,2238,2170,2351,1088,2191,1204,1812,1468,2470,882,2177,2655,1014,1870,972,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL776-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 16:00:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.07 % [INFO] Parsing done (236ms).
% 1.85/1.08 % [INFO] Running in sequential loop mode.
% 2.33/1.28 % [INFO] eprover registered as external prover.
% 2.33/1.29 % [INFO] cvc4 registered as external prover.
% 2.33/1.29 % [INFO] Scanning for conjecture ...
% 2.84/1.42 % [INFO] Found a conjecture and 866 axioms. Running axiom selection ...
% 3.52/1.57 % [INFO] Axiom selection finished. Selected 866 axioms (removed 0 axioms).
% 4.08/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 4.08/1.77 % [INFO] Type checking passed.
% 4.42/1.77 % [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 ...
% 16.15/4.44 % External prover 'cvc4' found a proof!
% 16.15/4.44 % [INFO] Killing All external provers ...
% 16.15/4.44 % Time passed: 3923ms (effective reasoning time: 3354ms)
% 16.15/4.44 % 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)>
% 16.15/4.45 % Axioms used in derivation (866): cls_Nil__is__rev__conv_1, cls_not__one__less__zero_0, cls_last_Osimps_0, cls_less__iff__diff__less__0_0, cls_sgn__less_0, cls_linorder__antisym__conv2_1, cls_append__eq__append__conv__if_3, cls_subst__lt_0, cls_power__0_0, cls_App__eq__foldl__conv_3, cls_le__0__eq_1, cls_take__eq__Nil_0, cls_less__divide__eq_3, cls_butlast__snoc_0, cls_Suc__pred_0, cls_list__update__same__conv_1, cls_add__0__left_0, cls_last__drop_0, cls_xt1_I9_J_0, cls_add__pos__nonneg_0, cls_nth__list__update__neq_0, cls_le__divide__eq_3, cls_dB_Osimps_I6_J_0, cls_length__0__conv_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_rev__swap_1, cls_last_Osimps_1, cls_less__diff__iff_1, cls_zero__less__one_0, cls_divide__le__eq_2, cls_class__ringb_Oadd__r0__iff_1, cls_Cons__eq__append__conv_2, cls_add__less__cancel__left_1, cls_Suc__inject_0, cls_eq__imp__le_0, cls_nth__Cons_H_0, cls_Suc__mono_0, cls_Cons__eq__append__conv_5, cls_Var__eq__apps__conv_1, cls_nth__Cons__number__of_0, cls_le__diff__iff_0, cls_zero__less__divide__iff_5, cls_lists__accI_0, cls_of__nat__0_0, cls_subst__eq_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, cls_subst__App_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_Cons__step1__Cons_0, cls_divide__less__0__iff_0, cls_div__le__mono_0, cls_list__update__overwrite_0, cls_Nat_Odiff__diff__eq_0, cls_divide__self_0, cls_append__self__conv_0, cls_butlast_Osimps_I1_J_0, cls_take__Suc__conv__app__nth_0, cls_termi__implies__IT_0, cls_divide__nonpos__neg_0, cls_drop__append_0, cls_zero__le__one_0, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, cls_dB_Osimps_I8_J_0, cls_negative__imp__inverse__negative_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_take__0_0, cls_diff__Suc__1_0, cls_take__tl_0, cls_nth__take_0, cls_eq__diff__iff_0, cls_less__half__sum_0, cls_replicate__empty_0, cls_power__inject__exp_0, cls_tl_Osimps_I1_J_0, cls_nth__list__update__eq_0, cls_power__increasing_0, cls_of__nat__less__iff_0, cls_nonzero__inverse__eq__divide_0, clsarity_Int__Oint__OrderedGroup_Omonoid__add, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_inverse__eq__iff__eq_0, cls_append__step1I_0, cls_linorder__neqE_0, cls_divide__1_0, cls_add__strict__right__mono_0, clsarity_Int__Oint__Orderings_Oorder, cls_less__antisym_0, cls_conversepD_0, cls_inverse__le__1__iff_2, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_take__Cons_H_0, clsarity_fun__Orderings_Oorder, cls_rev__singleton__conv_1, cls_pos__add__strict_0, cls_accp__downwards_0, cls_zero__le__divide__iff_2, cls_zero__less__divide__iff_0, cls_add__le__cancel__left_1, cls_not__Cons__self2_0, cls_add__imp__eq_0, cls_divide__le__0__1__iff_1, cls_not__less__eq_1, cls_inverse__less__1__iff_2, cls_add__le__cancel__right_1, cls_sgn0_0, cls_div__add__self2_0, cls_nth__list__update_0, cls_rtrancl__beta__Abs_0, cls_less__divide__eq__number__of_3, cls_less__imp__inverse__less__neg_0, cls_Snoc__step1__SnocD_2, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_list__update__append_1, cls_less__Suc__eq_2, cls_frac__le_0, cls_rev__is__rev__conv_0, cls_one__le__inverse__iff_2, cls_not__step1__Nil_0, cls_appR_0, cls_inverse__1_0, cls_append__eq__append__conv__if_6, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_listsp_ONil_0, cls_hd__conv__nth_0, cls_split__div_H_6, cls_order__less__trans_0, cls_self__append__conv_0, cls_of__nat__0__less__iff_0, cls_eq__divide__eq__number__of_1, cls_add__left__cancel_0, cls_power__less__imp__less__exp_0, cls_head__Var__reduction_1, cls_comm__monoid__add_Omult__1__right_0, cls_drop__0_0, cls_power__le__imp__le__exp_0, cls_nth__Cons_H_1, cls_list__update__nonempty_1, cls_power__one_0, cls_id__take__nth__drop_0, cls_power__gt1_0, cls_append__eq__Cons__conv_4, cls_add__nonpos__neg_0, cls_eq__Nil__appendI_0, cls_comm__monoid__add_Omult__assoc_0, cls_rtranclp__trans_0, cls_Cons__step1__Cons_5, cls_add__cancel__21_1, cls_same__append__eq_0, cls_take__Cons__number__of_1, cls_beta_0, cls_gr0I_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_split__div_5, cls_length__butlast_0, cls_subst__preserves__beta_0, cls_hd__append_0, cls_inverse__divide_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_add__nonneg__pos_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_append__Cons_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_div__by__0_0, cls_butlast_Osimps_I2_J_1, cls_le__0__eq_0, cls_divide__le__0__iff_3, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_rotate1__length01_0, cls_drop__Cons__number__of_0, clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add, cls_replicate__eq__replicate_0, cls_append__eq__append__conv__if_2, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_gr__implies__not0_0, cls_diff__diff__cancel_0, cls_less__divide__eq__number__of1_2, cls_of__nat__le__iff_1, cls_divide__neg__neg_0, cls_nat__less__cases_0, cls_rev__drop_0, cls_rev__take_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_append__eq__Cons__conv_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_field__power__not__zero_0, cls_Var__apps__eq__Var__apps__conv_0, cls_right__inverse__eq_0, clsarity_nat__Divides_Osemiring__div, cls_one__le__power_0, cls_diff__le__mono2_0, cls_Suc__le__mono_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_tl__replicate_0, cls_order__less__asym_0, cls_butlast__list__update_0, cls_nth__Cons__Suc_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_le__antisym_0, cls_add__right__mono_0, cls_append1__eq__conv_1, cls_less__iff__diff__less__0_1, cls_inverse__le__1__iff_1, cls_order__eq__refl_0, cls_subst__gt_0, cls_order__le__less_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_eq__number__of_0, cls_length__greater__0__conv_1, cls_of__nat__le__iff_0, cls_inverse__eq__1__iff_1, clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add, cls_sgn__pos_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_div__self_0, cls_linorder__antisym__conv2_0, cls_le__div__geq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_class__fieldgb_Oinverse__divide_0, cls_dB_Osimps_I3_J_0, cls_replicate__append__same_0, cls_list__update__beyond_0, cls_power__one__over_0, cls_foldl__absorb0_0, cls_Suc__leI_0, cls_nth__via__drop_0, cls_linorder__neqE__nat_0, cls_hd__append_1, cls_list__update__append1_0, cls_take__1__Cons_0, cls_rev__singleton__conv_0, cls_inverse__nonpositive__iff__nonpositive_0, cls_inverse__nonnegative__iff__nonnegative_1, cls_rev_Osimps_I2_J_0, 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cls_nonzero__inverse__inverse__eq_0, cls_list__update__id_0, cls_rtranclp_Ortrancl__refl_0, cls_div__0_0, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_Suc__lessD_0, cls_order__less__le_2, cls_list_Osimps_I3_J_0, cls_nat__neq__iff_0, cls_le__less__Suc__eq_0, clsarity_Int__Oint__Int_Onumber__ring, cls_zero__less__diff_0, cls_le0_0, cls_less__eq__Suc__le_1, cls_Suc__length__conv_2, clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add, cls_app__last_0, cls_rotate1__hd__tl_0, cls_class__semiring_Osemiring__rules_I33_J_0, cls_less__Suc__eq__le_0, cls_xt1_I11_J_0, cls_zero__le__divide__iff_0, cls_add__neg__neg_0, cls_eq__divide__eq__number__of_2, cls_split__div_0, cls_inverse__eq__divide__number__of_0, cls_drop__Suc_0, cls_rev__is__Nil__conv_1, cls_nonzero__inverse__eq__imp__eq_0, cls_le__eqI_0, cls_App__eq__foldl__conv_2, clsarity_Int__Oint__Ring__and__Field_Osgn__if, cls_last__replicate_0, cls_length__rotate1_0, cls_diff__self__eq__0_0, cls_append__eq__conv__conj_1, cls_Cons__acc__step1I_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_divide__less__0__iff_5, cls_take__Suc__Cons_0, cls_abs_0, cls_less__Suc0_0, cls_Snoc__step1__SnocD_0, cls_sgn__sgn_0, cls_divide__less__0__iff_2, cls_take__butlast_0, cls_rtranclp__idemp_0, cls_append__is__Nil__conv_1, cls_typing_OVar_0, cls_diff__Suc__less_0, cls_nat__less__le_0, cls_replicate__eq__replicate_2, cls_IT_OVar_0, clsarity_Int__Oint__OrderedGroup_Omonoid__mult, cls_last__conv__nth_0, cls_divide__less__eq__number__of_3, cls_accp__downward_0, cls_nth__Cons__number__of_1, cls_comm__monoid__add_Omult__left__commute_0, cls_apps__eq__tail__conv_0, cls_le__divide__eq__number__of1_3, cls_diff__divide__distrib_0, cls_Abs__eq__apps__conv_2, cls_diff__0__right_0, cls_xt1_I6_J_0, clsarity_Int__Oint__Nat_Osemiring__char__0, cls_positive__imp__inverse__positive_0, cls_le__add__right__mono_0, cls_inverse__inverse__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_divide__eq__eq__number__of1_1, cls_diff__le__self_0, cls_power__one__right_0, cls_nat_Osimps_I3_J_0, cls_apps__preserves__beta2_0, cls_zero__le__divide__1__iff_1, cls_le__Suc__eq_2, cls_comm__monoid__add_Omult__1_0, cls_length__drop_0, cls_linorder__not__le_0, cls_sgn__less_1, cls_Cons__eq__appendI_0, clsarity_Int__Oint__Ring__and__Field_Oidom, cls_double__add__less__zero__iff__single__less__zero_1, cls_accp_Ocases_0, cls_diff__less__mono2_0, cls_length__tl_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_one__less__inverse__iff_0, cls_lists__accD_0, cls_less__trans__Suc_0, cls_zero__less__divide__1__iff_1, cls_inverse__less__1__iff_1, cls_Nil__is__rev__conv_0, cls_nat__less__le_2, cls_divide__le__0__iff_4, cls_apps__preserves__beta_0, cls_order__less__irrefl_0, cls_gt__half__sum_0, cls_add__nonneg__eq__0__iff_2, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_less__diff__iff_0, cls_append__eq__appendI_0, cls_power__Suc__less__one_0, cls_less__eqI_0, cls_App__eq__foldl__conv_5, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_minus__nat_Odiff__0_0, cls_butlast_Osimps_I2_J_0, cls_append__eq__append__conv__if_0, cls_divide__less__0__iff_1, cls_frac__less2_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_Cons__eq__append__conv_4, cls_App__eq__foldl__conv_4, cls_length__Suc__conv_2, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_divide__le__eq__number__of1_3, cls_append__is__Nil__conv_0, cls_one__less__inverse__iff_1, cls_power__eq__0__iff_0, cls_eq__eqI_1, cls_Suc__n__not__le__n_0, cls_class__semiring_Oadd__c_0, cls_Abs__eq__apps__conv_0, cls_singleton__rev__conv_1, cls_list_Oinject_1, cls_zero__less__diff_1, cls_nonzero__power__divide_0, cls_one__less__power_0, clsarity_Int__Oint__OrderedGroup_Oab__group__add, cls_div__if_0, cls_power__less__imp__less__base_0, cls_rev__append_0, cls_n__not__Suc__n_0, cls_butlast__take_0, cls_Cons__eq__append__conv_1, cls_inverse__le__imp__le_0, cls_rev__nth_0, cls_take__Cons__number__of_0, cls_inverse__zero_0, cls_foldl__append_0, clsarity_Int__Oint__Divides_Osemiring__div, cls_Suc__leD_0, cls_inverse__less__imp__less__neg_0, clsarity_fun__Orderings_Opreorder, cls_le__diff__iff_1, cls_zero__less__divide__iff_4, cls_add__pos__pos_0, cls_inverse__eq__divide_0, cls_hd_Osimps_0, cls_add__mono_0, cls_divide__le__0__iff_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add, cls_power__inject__base_0, cls_less__divide__eq__number__of_2, cls_sgn__1__pos_0, cls_less__SucI_0, cls_drop__take_0, cls_add__neg__nonpos_0, cls_take__all_0, cls_not__less0_0, cls_nth__append__length_0, cls_dB_Osimps_I5_J_0, clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_class__semiring_Osemiring__rules_I24_J_0, cls_rev__swap_0, cls_eq__iff__diff__eq__0_1, cls_conversep__eq_0, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_append__replicate__commute_0, cls_append__eq__append__conv__if_5, cls_hd__rev_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_diffs0__imp__equal_0, cls_frac__less_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add, cls_expand__Suc_0, cls_add__less__cancel__left_0, cls_tl__drop_0, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_tl_Osimps_I2_J_0, cls_divide__eq__eq__number__of_2, cls_foldl__Nil_0, cls_Suc__less__eq_0, cls_le__iff__diff__le__0_1, cls_zero__le__power_0, cls_divide__less__eq__number__of_2, cls_take__Suc_0, cls_Suc__pred_H_0, cls_le__eqI_1, cls_Lambda_0, cls_class__semiring_Opwr__0_0, cls_Suc__diff__le_0, cls_impossible__Cons_0, cls_length__replicate_0, cls_divide__nonpos__pos_0, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_power__increasing__iff_0, cls_divide__less__eq_3, cls_rev__eq__Cons__iff_0, cls_sgn__if_1, clsarity_nat__Ring__and__Field_Osemiring__1, cls_nonzero__power__inverse_0, cls_nth__list__update_1, cls_inverse__less__imp__less_0, cls_order__less__imp__le_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_subst__Var_0, cls_inverse__positive__imp__positive_0, clsarity_Int__Oint__Ring__and__Field_Osemiring__1, cls_le__imp__inverse__le__neg_0, cls_diff__commute_0, cls_le__less__Suc__eq_1, cls_add__strict__increasing2_0, cls_le__eq__less__or__eq_0, cls_eq__iff__diff__eq__0_0, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_drop__all_0, cls_less__Suc0_1, cls_divide__eq__eq_1, cls_drop__eq__Nil_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, cls_append__eq__Cons__conv_3, cls_list__update__code_I3_J_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_order__less__le_1, cls_xt1_I7_J_0, cls_inverse__nonpositive__iff__nonpositive_1, cls_linorder__not__less_1, cls_appL_0, cls_nat__less__le_1, cls_Beta_0, cls_rev__rev__ident_0, cls_nth__replicate_0, cls_divide__less__0__1__iff_1, cls_add__le__cancel__left_0, cls_empty__replicate_1, cls_Snoc__step1__SnocD_1, cls_power__decreasing_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_le__neq__implies__less_0, cls_drop__Cons_H_1, cls_not__one__le__zero_0, cls_conversep__iff_1, cls_upd__conv__take__nth__drop_0, cls_subst__preserves__beta2_H_0, cls_list_Osimps_I2_J_0, cls_rtranclp__converseD_0, clsarity_nat__OrderedGroup_Osemigroup__add, cls_conversep_Ocases_0, clsarity_Int__Oint__OrderedGroup_Osemigroup__add, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_zero__le__divide__1__iff_0, cls_le__refl_0, cls_power__0__left_1, cls_double__induction__lemma_0, cls_list__update__nonempty_0, cls_rtrancl__beta__AppR_0, cls_power__mono_0, cls_App__eq__foldl__conv_1, cls_of__nat__less__0__iff_0, cls_divide__le__0__1__iff_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_divide__le__eq__number__of_3, cls_not__less__eq__eq_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_add__le__cancel__right_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0, cls_divide__less__0__iff_4, cls_rtranclp__converseI_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_div__if_1, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1
% 16.15/4.45 % No. of inferences in proof: 1743
% 16.15/4.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3923 ms resp. 3354 ms w/o parsing
% 16.71/4.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.71/4.77 % [INFO] Killing All external provers ...
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