TSTP Solution File: LCL795-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:31:46 EDT 2023
% Result : Unsatisfiable 14.59s 4.38s
% Output : Refutation 15.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1041
% Syntax : Number of formulae : 1960 ( 413 unt; 123 typ; 0 def)
% Number of atoms : 4391 (1156 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 27078 (2436 ~;2554 |; 0 &;22088 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 186 ( 186 >; 0 *; 0 +; 0 <<)
% Number of symbols : 125 ( 123 usr; 18 con; 0-6 aty)
% Number of variables : 5742 ( 0 ^;5742 !; 0 ?;5742 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(v_e_____type,type,
v_e____: $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_T_H_H_____type,type,
v_T_H_H____: $i ).
thf(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(v_u_____type,type,
v_u____: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i ).
thf(c_List_Ofoldr_type,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(v_Ts_____type,type,
v_Ts____: $i ).
thf(v_T_H_____type,type,
v_T_H____: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Orderings_Oord__class_Omin_type,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_List_Oappend_type,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
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_Suc_type,type,
c_Suc: $i > $i ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_Orderings_Oord__class_Omax_type,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $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_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(c_List_Oreplicate_type,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(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(v_n_____type,type,
v_n____: $i ).
thf(v_i_____type,type,
v_i____: $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(c_Type_Otype_OAtom_type,type,
c_Type_Otype_OAtom: $i > $i ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(c_Groebner__Basis_Ogb__semiring_type,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_Type_Otypings_type,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(v_T_____type,type,
v_T____: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_Nitpick_Onat__gcd_type,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(c_Type_Osko__Type__Xtyping__elims__2__1_type,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Type_Osko__Type__Xlist__app__typeD__1__1_type,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_Type_Otype_Otype__case_type,type,
c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(c_Type_Osko__Type__Xtype__induct__1__1_type,type,
c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(v_sko__Nat__Xnat__Xinducts__1_type,type,
v_sko__Nat__Xnat__Xinducts__1: $i > $i ).
thf(c_Type_Otype_Otype__rec_type,type,
c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_List_Olistsum_type,type,
c_List_Olistsum: $i > $i > $i ).
thf(v_sko__Nat__Xnat__Xinduct__1_type,type,
v_sko__Nat__Xnat__Xinduct__1: $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1: $i > $i > $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1_type,type,
c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_type,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(v_sko__List__Xreplicate__Xinduct__1_type,type,
v_sko__List__Xreplicate__Xinduct__1: $i > $i ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_Type_Osko__Type__Xtyping__elims__3__1_type,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xtyping__elims__3__2_type,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).
thf(c_Type_Osko__Type__Xlist__app__typeE__1__1_type,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(v_a_____type,type,
v_a____: $i ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(v_sko__List__Xupt__Xinduct__1_type,type,
v_sko__List__Xupt__Xinduct__1: $i > $i ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(c_nat_Onat__size_type,type,
c_nat_Onat__size: $i > $i ).
thf(c_Nat_Onat_Onat__rec_type,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_Type_Osko__Type__Xabs__typeE__1__1_type,type,
c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).
thf(c_Type_Osko__Type__Xabs__typeE__1__2_type,type,
c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(c_Nat_Osize__class_Osize_type,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_String_Ochar_type,type,
tc_String_Ochar: $i ).
thf(v_as_____type,type,
v_as____: $i ).
thf(c_String_Ochar_Ochar__size_type,type,
c_String_Ochar_Ochar__size: $i > $i ).
thf(521,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(819,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(2822,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(1411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(728,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(2612,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(801,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(2778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(2072,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(1237,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)],[128]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[408]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(539,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(2199,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(586,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ F @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(2295,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ F @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(2341,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ D ) @ E @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
thf(2336,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ D ) @ E @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(900,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(3008,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(1315,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(720,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(2595,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(677,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D )
= ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(2427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D )
= ( c_List_Oappend @ ( c_List_Oreplicate @ A @ C @ D ) @ ( c_List_Oreplicate @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(962,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(317,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(1686,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(2250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(1750,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)],[346]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__induct_1) ).
thf(1924,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(877,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(2953,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(117,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(1205,plain,
v_n____ = v_i____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(834,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(2854,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1692,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ B @ A @ C ) @ tc_Type_Otype ) @ C @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ B @ A @ C ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ B @ A @ C ) @ tc_Type_Otype ) @ C @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ B @ A @ C ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(2104,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(813,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) )
| ~ ( c_lessequals @ A @ D @ tc_nat )
| ( C
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
thf(2808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) )
| ~ ( c_lessequals @ A @ D @ tc_nat )
| ( C
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(1522,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)],[243]) ).
thf(800,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(2776,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
thf(1808,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(753,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ A @ B ) @ tc_Type_Otype ) @ B @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
thf(2671,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ A @ B ) @ tc_Type_Otype ) @ B @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ A @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(254,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(1544,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(2014,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(826,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2837,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(1671,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)],[311]) ).
thf(782,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(2740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(917,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(3044,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(2448,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)],[656]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(2434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(2168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_ONil @ B ) @ C @ B @ D )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(297,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ B ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ F @ G @ E @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(1640,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ B ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ F @ G @ E @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(431,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(1954,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(1458,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)],[217]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(1497,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)],[233]) ).
thf(537,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
thf(2195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(904,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(3017,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(349,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ D @ A @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
thf(1756,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ D @ A @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(1310,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)],[158]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(1867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(2184,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(450,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1999,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)],[450]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
thf(2316,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oreplicate @ B @ C @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(1919,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)],[416]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(1988,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(660,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(2459,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(855,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(2901,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_2) ).
thf(1746,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(546,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
thf(2216,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_Suc @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit_1) ).
thf(1576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_Suc @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(2082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(690,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(2531,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(840,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(2869,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(403,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 @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(1887,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 @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2432,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)],[648]) ).
thf(414,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(1914,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(793,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(2763,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(2548,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)],[699]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1724,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)],[335]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(1475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(820,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( B = E )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(2825,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)],[820]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(1967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(1628,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)],[291]) ).
thf(328,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1709,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(602,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(2328,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(2039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Lambda_Obeta @ D @ B )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(789,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2755,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)],[789]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(1871,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ A @ B @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(1455,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)],[216]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(2488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate_Oinduct_1) ).
thf(1992,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(1059,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)],[59]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Olist_ONil @ B ) @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(1409,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)],[198]) ).
thf(780,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
thf(2735,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(2814,plain,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(444,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(1985,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)],[444]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(1264,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)],[139]) ).
thf(547,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(2217,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(785,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(2745,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(709,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(2571,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(642,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(2420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(835,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(2857,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(795,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(2767,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(1568,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(686,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(2520,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(2158,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)],[519]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(2301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(2852,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)],[833]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_Suc @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit__asm_1) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_Suc @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(2691,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(622,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(2373,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)],[622]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(1572,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(867,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(2929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(891,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2989,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(550,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(2222,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1911,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)],[413]) ).
thf(744,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(2650,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(504,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(2122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(1978,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)],[441]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(1383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(966,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1946,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)],[427]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(1465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(1664,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)],[308]) ).
thf(807,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(2794,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(599,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(2324,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1714,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)],[331]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(2027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(851,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(2893,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(1632,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(2469,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(2451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(558,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(1682,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(1136,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(313,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
thf(1677,plain,
( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(695,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(2540,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(2034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(434,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(1960,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(2555,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)],[702]) ).
thf(475,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(2058,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(2523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(510,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(882,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(2965,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(2205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(888,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(2982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(792,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(2762,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(619,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(2367,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(1928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(2833,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)],[824]) ).
thf(578,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ D ) @ E @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
thf(2281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ D ) @ E @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(644,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
thf(2424,plain,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(2371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(798,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(2772,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)],[798]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_2) ).
thf(2639,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(77,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(1104,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)],[77]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ( 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 ) )
| ~ ( c_InductTermi_OIT @ B )
| ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ( 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 ) )
| ~ ( c_InductTermi_OIT @ B )
| ~ ( 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)],[323]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(1242,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)],[130]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( c_Type_Otype_OAtom @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(2574,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( c_Type_Otype_OAtom @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(2646,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)],[742]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(2047,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(555,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(2232,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(2641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(281,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1604,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(864,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(2922,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(222,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(1470,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(491,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ C @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(2093,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ C @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(360,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(1783,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(781,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(2737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(2496,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(749,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ A @ B @ C ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ B @ ( c_Lambda_OdB_OAbs @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(2660,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ A @ B @ C ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ B @ ( c_Lambda_OdB_OAbs @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(1768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ B @ D ) ) @ C ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(1636,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)],[295]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1730,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(913,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(1057,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)],[58]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) @ ( c_Lambda_Osubst @ D @ B @ C ) )
| ~ ( c_Lambda_Obeta @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(717,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(2589,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(637,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(2409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1091,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)],[72]) ).
thf(723,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_0) ).
thf(2601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(696,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
thf(2541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1580,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)],[270]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
thf(2606,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(2032,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(689,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(2528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ C )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(2396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(2441,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)],[652]) ).
thf(754,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(2673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(957,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)],[16]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ D @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(1223,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)],[123]) ).
thf(172,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) ) @ E ) @ F @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(1343,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) ) @ E ) @ F @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(812,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(2805,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
thf(1570,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( C
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(1174,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)],[105]) ).
thf(907,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(3022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[907]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(1502,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)],[235]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(2150,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(1370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(2414,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(2132,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)],[508]) ).
thf(849,axiom,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(2890,plain,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(879,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(2958,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(654,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2445,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(318,axiom,
! [B: $i,A: $i] : ( 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/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(1687,plain,
! [B: $i,A: $i] : ( 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)],[318]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(2068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[479]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ D @ B @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(974,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)],[23]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(2653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(2464,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1837,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(280,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(1602,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(2663,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(818,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(2820,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)],[818]) ).
thf(841,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(2872,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)],[841]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(1951,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(119,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Oreplicate @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(1210,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)],[119]) ).
thf(305,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(1656,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(601,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2327,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(910,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(3028,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ B ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ C @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(609,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(2345,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)],[609]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(1195,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)],[113]) ).
thf(544,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ E ) @ D ) )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(2211,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ E ) @ D ) )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1128,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(674,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
thf(2492,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(553,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(2228,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)],[553]) ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(2112,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)],[499]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(500,axiom,
( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
thf(2115,plain,
( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(368,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(1804,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(712,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omin @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
thf(2577,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omin @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(763,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(2694,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(776,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(2726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(1118,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)],[82]) ).
thf(572,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(2268,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(2245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(1350,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)],[175]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(1089,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)],[71]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(1762,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)],[351]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) @ B ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(2515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ) @ B ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
thf(1772,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(1259,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)],[137]) ).
thf(892,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(2990,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(1794,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(430,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(1953,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(759,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(2685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[759]) ).
thf(828,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2841,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(616,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/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(2359,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)],[616]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(769,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(2709,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(1970,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)],[438]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(2509,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(693,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2537,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(905,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(3018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ C @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ C @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(1659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(897,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(3000,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(705,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(2561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(822,axiom,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(2830,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1739,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)],[341]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(1075,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(272,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1584,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(2613,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(2108,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(404,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(1889,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(802,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(2781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ C @ D ) @ D )
= ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(1493,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)],[231]) ).
thf(809,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(2798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(1160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(843,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(2877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[843]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(1424,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)],[204]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(2312,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(901,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(3010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(560,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(2240,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(525,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/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(2172,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)],[525]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(1810,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)],[371]) ).
thf(363,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(1791,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(700,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(2551,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( c_List_Olist_OCons @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(285,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(1612,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(2304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1131,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(55,axiom,
! [A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(1050,plain,
! [A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(679,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__rec @ A @ B @ ( c_Suc @ C ) @ D )
= ( hAPP @ ( hAPP @ B @ C ) @ ( c_Nat_Onat_Onat__rec @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__Suc_0) ).
thf(2505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__rec @ A @ B @ ( c_Suc @ C ) @ D )
= ( hAPP @ ( hAPP @ B @ C ) @ ( c_Nat_Onat_Onat__rec @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(453,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(2006,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(1874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(899,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ E @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(3005,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ B @ F @ G @ E @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(2140,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1525,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)],[244]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(1825,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)],[379]) ).
thf(883,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(2968,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)],[883]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(1324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(580,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
thf(2285,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__List__Xreplicate__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(274,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(1588,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)],[274]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
thf(1099,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(985,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)],[27]) ).
thf(692,axiom,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(2536,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(1297,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(250,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(1539,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(628,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(2387,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_List_Oappend @ B @ A @ C ) )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(1231,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)],[126]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
thf(2153,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(854,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2900,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(258,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) )
= B )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) )
= B )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(561,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(2243,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(2355,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(112,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1192,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(707,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(2566,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
thf(1799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(34,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) ) @ E ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(1002,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) ) @ E ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(837,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(2862,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(350,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1759,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(191,axiom,
! [A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(1393,plain,
! [A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(1333,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)],[168]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(866,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2926,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)],[866]) ).
thf(698,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(2546,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(543,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(2208,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(1712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(634,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(2402,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(2089,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)],[489]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(2617,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)],[731]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(1732,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(737,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(2634,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)],[737]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(2749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
= ( c_List_Olist_OCons @ B @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(1434,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)],[208]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1202,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)],[116]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(2203,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(1814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(846,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(2883,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(881,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(2963,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= B )
| ( A
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(1035,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)],[49]) ).
thf(620,axiom,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(2368,plain,
! [B: $i,A: $i] :
( ( A
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(861,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2915,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(1895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinducts_1) ).
thf(2189,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ A ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(894,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2995,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)],[894]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(2338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(449,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(1996,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(2909,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(503,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(2121,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ A @ B @ C ) @ D @ C )
= ( c_List_Olist_OCons @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(1278,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)],[145]) ).
thf(451,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ B @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(527,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_headT_0) ).
thf(2176,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(584,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(2292,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).
thf(2391,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) @ ( c_Lambda_Olift @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(916,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(3042,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(872,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(2941,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)],[872]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(1548,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(623,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/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2376,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)],[623]) ).
thf(569,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/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(2260,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)],[569]) ).
thf(870,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2936,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)],[870]) ).
thf(777,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(2729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(1727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(1510,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(772,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(2717,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(122,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(1219,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)],[122]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(1595,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(779,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_argT_0) ).
thf(2734,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(1154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(836,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(2859,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(1884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ( B = C )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(806,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(2791,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ E )
= ( hAPP @ A @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ E @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(688,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(2525,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ B @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(458,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(2016,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)],[458]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(248,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(1535,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Olist_OCons @ B @ C @ D ) @ E @ D @ F )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(1701,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(436,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(1965,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldr @ A @ ( c_List_Oappend @ B @ C @ D ) @ E @ D @ F )
= ( c_List_Ofoldr @ A @ B @ ( c_List_Ofoldr @ A @ C @ E @ D @ F ) @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(805,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(631,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(2393,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(347,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1752,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(2161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(1786,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)],[361]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(2220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__case @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(1312,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)],[159]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(1865,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)],[395]) ).
thf(898,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(3002,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)],[898]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(791,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(2759,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)],[791]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(2425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(666,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2474,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(296,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(1638,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)],[296]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(2891,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(591,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_OCons @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(2308,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)],[591]) ).
thf(659,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(2457,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(407,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1897,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1,negated_conjecture,
~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(919,plain,
~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(703,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(2557,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(177,axiom,
! [A: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_List_Olist_ONil @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(1356,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)],[177]) ).
thf(710,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2573,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(2346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(2079,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(694,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(890,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__drop_0) ).
thf(2987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(1574,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)],[267]) ).
thf(799,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(878,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(2955,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)],[878]) ).
thf(252,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1542,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(1043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(811,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2802,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)],[811]) ).
thf(84,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1122,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1439,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(2197,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(774,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(2721,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)],[774]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(2119,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)],[502]) ).
thf(147,axiom,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(668,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(2084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(545,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(2383,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)],[626]) ).
thf(738,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(2637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[738]) ).
thf(643,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(2422,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(857,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(2906,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)],[857]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(1048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(568,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(2257,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(1933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(873,axiom,
! [A: $i] :
( ( c_String_Ochar_Ochar__size @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_char__size_0) ).
thf(2943,plain,
! [A: $i] :
( ( c_String_Ochar_Ochar__size @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(852,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(2896,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(529,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__induct_0) ).
thf(2180,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(2182,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(400,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(1877,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)],[400]) ).
thf(783,axiom,
c_InductTermi_OIT @ v_u____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(2742,plain,
c_InductTermi_OIT @ v_u____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(1630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(1862,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(912,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(3034,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)],[912]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(1029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(842,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(2874,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ C ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(943,plain,
! [B: $i,A: $i] :
( ( c_List_Oappend @ A @ ( c_List_Olist_ONil @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(885,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(2974,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(2025,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(2632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(1339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2610,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)],[727]) ).
thf(594,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
thf(2314,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lem0_0) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(2446,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(790,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
thf(2757,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(1460,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)],[218]) ).
thf(582,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(2289,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)],[582]) ).
thf(577,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(2278,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(701,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(2553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ C @ A @ B @ D ) @ C @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1381,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)],[186]) ).
thf(859,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(2911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1112,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)],[80]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1688,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(1699,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)],[324]) ).
thf(825,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(2835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( c_Type_Otype_OAtom @ D ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(487,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(2086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ B )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ B )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(477,axiom,
! [B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
thf(2064,plain,
! [B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(868,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(2101,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)],[494]) ).
thf(896,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2999,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(262,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) )
| ~ ( c_Type_Otyping @ F @ D @ A )
| ~ ( c_InductTermi_OIT @ D )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
| ~ ( c_InductTermi_OIT @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(1562,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) )
| ~ ( c_Type_Otyping @ F @ D @ A )
| ~ ( c_InductTermi_OIT @ D )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ A @ tc_Type_Otype ) @ C @ G )
| ~ ( c_InductTermi_OIT @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(797,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(2770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( c_Type_Otype_OAtom @ C ) @ D )
= ( hAPP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(641,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(2418,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)],[641]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(1926,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(2365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(472,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ E @ F @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(2051,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ C @ ( hAPP @ ( hAPP @ A @ D ) @ D ) ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ C @ E @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(794,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( 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 @ ( c_Orderings_Oord__class_Omin @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff_0) ).
thf(2765,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( 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 @ ( c_Orderings_Oord__class_Omin @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1245,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)],[131]) ).
thf(669,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ F @ A @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).
thf(2481,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ F @ A @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(732,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(2620,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)],[732]) ).
thf(562,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(2244,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(788,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(2752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(1364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(889,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ C @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(2984,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ C @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1973,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(2054,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(2096,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(751,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(2665,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(2471,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)],[665]) ).
thf(466,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(2037,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otypings @ A @ B @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ D @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1134,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)],[88]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(2629,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(446,axiom,
! [B: $i,A: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= ( c_List_Olist_ONil @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(1990,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)],[446]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(1472,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)],[223]) ).
thf(853,axiom,
! [A: $i] : ( c_lessequals @ A @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
thf(2899,plain,
! [A: $i] : ( c_lessequals @ A @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(714,axiom,
! [A: $i] :
( ( c_nat_Onat__size @ ( c_Suc @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osize_I2_J_0) ).
thf(2582,plain,
! [A: $i] :
( ( c_nat_Onat__size @ ( c_Suc @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ A ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(911,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(3031,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(816,axiom,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ A @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_size__char_0) ).
thf(2816,plain,
! [A: $i] :
( ( c_Nat_Osize__class_Osize @ A @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(2318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(411,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(1905,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( ( c_Type_Otype_OAtom @ A )
!= ( c_Type_Otype_OAtom @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( ( c_Type_Otype_OAtom @ A )
!= ( c_Type_Otype_OAtom @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(505,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(2124,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(557,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
thf(2234,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(604,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ B @ C ) @ ( c_Suc @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ B @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
thf(2333,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ C )
= ( hAPP @ ( hAPP @ B @ C ) @ ( c_Suc @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ B @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(830,axiom,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(2846,plain,
! [B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(721,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(2597,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(1958,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(683,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
thf(2513,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(1748,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(2298,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)],[587]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(1770,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(886,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(2977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
| ( B = D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(456,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(2012,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(300,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1647,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(1780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(845,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2882,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1598,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)],[278]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1225,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)],[124]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(1743,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(1941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ A @ B @ C ) @ ( c_List_Oreplicate @ D @ B @ C ) @ C )
= ( c_List_Oappend @ ( c_List_Oreplicate @ D @ B @ C ) @ ( c_List_Oreplicate @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(1252,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)],[134]) ).
thf(756,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(2678,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)],[756]) ).
thf(685,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(2518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[685]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(1753,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)],[348]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(2407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(627,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(2386,plain,
class_OrderedGroup_Osemigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(832,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(2850,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= A )
| ( B
= ( c_List_Olist_ONil @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(1484,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)],[228]) ).
thf(823,axiom,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(2831,plain,
! [A: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(761,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(2689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(786,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(2747,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(708,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(2569,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(2454,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)],[658]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(863,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
= ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(2920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ A @ B @ C @ D ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D )
= ( c_Type_Oshift @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ E @ D ) @ ( c_Suc @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ C ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__least__nat__le_1) ).
thf(1869,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ C ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(647,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(2429,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)],[647]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(1262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(409,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
thf(1901,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1679,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)],[314]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(2044,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)],[469]) ).
thf(915,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(3041,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(1336,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)],[169]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(1452,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)],[215]) ).
thf(576,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(2276,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omax @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(442,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ B @ A @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(1980,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ B @ A @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1085,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[598]) ).
thf(766,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__induct_1) ).
thf(2701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(671,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(2486,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(722,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__least__nat__le_2) ).
thf(2599,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(856,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Oreplicate @ A @ B @ C )
!= ( c_List_Olist_ONil @ C ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(2903,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)],[856]) ).
thf(875,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ C ) @ E ) )
= ( hAPP @ ( hAPP @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ B @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(2948,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ B @ C ) @ E ) )
= ( hAPP @ ( hAPP @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ B @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(2411,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)],[638]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osplit_0) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Nat_Onat_Onat__case @ B @ C @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(697,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(1284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(713,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ D @ A @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
thf(2579,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ D @ A @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(871,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(2939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2848,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[831]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) )
| ~ ( c_InductTermi_OIT @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(755,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(2675,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)],[755]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(2056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_OCons @ A @ B @ C )
!= ( c_List_Olist_OCons @ D @ E @ C ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(1358,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)],[178]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(2247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(253,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(1543,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(353,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1766,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(1849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(827,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(2838,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(2558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(176,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_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1353,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_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__rec @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__rec @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(829,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(2843,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(513,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) )
| ~ ( c_lessequals @ D @ A @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
thf(2145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) )
| ~ ( c_lessequals @ D @ A @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(597,axiom,
( ( c_nat_Onat__size @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osize_I1_J_0) ).
thf(2320,plain,
( ( c_nat_Onat__size @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omin @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(770,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( c_Power_Opower__class_Opower @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(2711,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)],[770]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(1585,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)],[273]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[682]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ A @ B @ C ) @ D @ C )
= ( c_List_Oappend @ A @ ( c_List_Oappend @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(978,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)],[24]) ).
thf(91,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(1140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(1797,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)],[365]) ).
thf(908,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(3024,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(332,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(1717,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(401,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( c_Suc @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ C @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
thf(1881,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( c_Suc @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ C @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_OCons @ A @ B @ C )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ C ) @ ( c_List_Olist_OCons @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(1272,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)],[142]) ).
thf(865,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
thf(2924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) ) @ E ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(1839,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)],[385]) ).
thf(488,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(2088,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(817,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
thf(2818,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(847,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(2696,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)],[764]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(1157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(536,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2194,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(1654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ C @ A @ D @ B ) )
| ~ ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ D ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2325,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(748,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(2658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(339,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(1734,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(734,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(2626,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(613,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(2352,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(1949,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)],[428]) ).
thf(821,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( v_sko__Nat__Xnat__Xinduct__1 @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
thf(2310,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(1844,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)],[387]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(895,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(2997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(673,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(2490,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Type_Otype_Otype__case @ B @ C @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ D ) @ E ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(533,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[533]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(190,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_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(1390,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_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(2226,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(741,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(2643,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(1108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(914,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(3039,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1326,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)],[165]) ).
thf(768,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(2707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1674,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)],[312]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2290,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)],[583]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(814,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(2811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ A @ E @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(884,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(2971,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)],[884]) ).
thf(391,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1854,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)],[391]) ).
thf(726,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(2608,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(377,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(1822,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(2416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(1276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(718,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(2591,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1590,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)],[275]) ).
thf(299,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_varT_0) ).
thf(1646,plain,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= ( c_Orderings_Oord__class_Omin @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ C @ A )
= ( c_Orderings_Oord__class_Omin @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(719,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_H_0) ).
thf(2594,plain,
c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(526,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(2174,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(579,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ B ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__least__nat__le_0) ).
thf(2283,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ A @ B ) @ B @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(2389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(171,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(1341,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_List_Olistsum @ B @ A ) ) @ ( c_List_Olistsum @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(2135,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_Suc @ C ) @ D )
= ( hAPP @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_Suc @ C ) @ D )
= ( hAPP @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ A )
!= ( c_List_Oappend @ B @ C @ A ) )
| ( B
= ( c_List_Olist_ONil @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(995,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)],[31]) ).
thf(869,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/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(2934,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)],[869]) ).
thf(516,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(2152,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(2262,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)],[570]) ).
thf(808,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(2796,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(603,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(2330,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)],[603]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
thf(2066,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(1706,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)],[327]) ).
thf(757,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/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(2680,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)],[757]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(1513,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)],[239]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).
thf(1661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(554,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2230,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ B )
= ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
thf(1994,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) ) @ B )
= ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(459,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(2019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ C @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(667,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(2475,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)],[667]) ).
thf(804,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2786,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)],[804]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ A ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(2399,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)],[633]) ).
thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(2041,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)],[468]) ).
thf(743,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(2648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1777,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)],[358]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(661,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(2462,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(1077,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)],[66]) ).
thf(617,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/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(2362,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)],[617]) ).
thf(675,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(2494,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(1444,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)],[212]) ).
thf(862,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(2917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ A ) )
| ( A = C )
| ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(2623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ D @ A )
= ( c_Power_Opower__class_Opower @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(548,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(581,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(357,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(1774,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(758,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(2683,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(146,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(1280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) ) @ F ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(269,axiom,
! [A: $i] :
( ( c_Nitpick_Onat__gcd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__gcd_Osimps_0) ).
thf(1578,plain,
! [A: $i] :
( ( c_Nitpick_Onat__gcd @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(773,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(2719,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)],[773]) ).
thf(556,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(2233,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(1546,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)],[255]) ).
thf(290,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(1625,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(876,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(2951,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(412,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(1908,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) ) @ D )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(2003,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(512,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(2142,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(518,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ E @ A @ F @ C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(2155,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= C )
| ~ ( c_Groebner__Basis_Ogb__semiring @ D @ E @ A @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(691,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(2534,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)],[691]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(2255,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil @ A )
!= ( c_List_Olist_OCons @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(950,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)],[13]) ).
thf(716,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(2587,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)],[716]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(1593,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(724,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(2604,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
thf(2008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ D @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(796,axiom,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2768,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(226,axiom,
! [A: $i] :
( ( c_List_Olist_ONil @ A )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ A ) @ ( c_List_Olist_ONil @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(1480,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)],[226]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(3015,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(810,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(2800,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(532,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(2186,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(2070,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(767,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(2704,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)],[767]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(771,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(2714,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(955,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[745]) ).
thf(803,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
thf(2783,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) ) @ E ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) ) @ C ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1859,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)],[393]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(1816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otype_Otype__rec @ A @ B @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) @ E )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ ( c_Type_Otype_Otype__rec @ A @ B @ C @ E ) ) @ ( c_Type_Otype_Otype__rec @ A @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1495,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_Lambda_OdB_OAbs @ B ) )
| ~ ( c_Lambda_Obeta @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(880,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
thf(2961,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(860,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(2913,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(490,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2091,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(635,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(2404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(551,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( B
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(752,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(2668,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)],[752]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(342,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1742,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(928,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)],[5]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otype_OAtom @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Type_Otype_OAtom @ A )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(778,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(2731,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)],[778]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(1152,plain,
! [B: $i,A: $i] :
( A
= ( c_List_Oappend @ ( c_List_Olist_ONil @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(247,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(1532,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ E @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1378,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)],[185]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(2467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[663]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(2507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ 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)],[680]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ ( c_Suc @ B ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(1505,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ ( c_Suc @ B ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1120,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(2502,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)],[678]) ).
thf(506,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(2127,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(909,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/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(3025,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)],[909]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(1827,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_List_Olistsum @ B @ A )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(1582,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)],[271]) ).
thf(571,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(2265,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ F @ A @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(1976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(257,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(1550,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ D )
| ~ ( c_Type_Otypings @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ E @ D @ tc_Type_Otype @ tc_Type_Otype ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(234,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Oappend @ C @ D @ E ) @ F @ E )
= ( c_List_Ofoldl @ A @ ( c_List_Ofoldl @ A @ B @ C @ F @ E ) @ D @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(1500,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)],[234]) ).
thf(906,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(3020,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)],[906]) ).
thf(760,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
thf(2687,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Omin @ ( 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)],[760]) ).
thf(838,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(2864,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) @ F ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(1004,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) ) @ F ) @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) ) @ F ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(2699,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(3013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ 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)],[902]) ).
thf(844,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) )
| ~ ( c_Type_Otyping @ F @ D @ B )
| ~ ( c_InductTermi_OIT @ D )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
| ~ ( c_InductTermi_OIT @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(2879,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ A ) @ B ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ C @ D @ E ) )
| ~ ( c_Type_Otyping @ F @ D @ B )
| ~ ( c_InductTermi_OIT @ D )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ F @ E @ B @ tc_Type_Otype ) @ C @ G )
| ~ ( c_InductTermi_OIT @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(1320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(1962,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(706,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ B @ A @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(2563,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ A @ D ) @ E ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ B @ A @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(839,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(2866,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(650,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(2436,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_Suc @ B ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(2106,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)],[496]) ).
thf(918,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
thf(3047,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ B @ C )
!= ( c_List_Oappend @ A @ D @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(1069,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)],[63]) ).
thf(887,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(2980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(282,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(1606,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)],[282]) ).
thf(303,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1653,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
thf(1944,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Nat_Onat_Onat__case @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(1367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Oappend @ A @ ( c_List_Olist_OCons @ B @ ( c_List_Olist_ONil @ C ) @ C ) @ C )
!= ( c_List_Oappend @ D @ ( c_List_Olist_OCons @ E @ ( c_List_Olist_ONil @ C ) @ C ) @ C ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(1009,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)],[37]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(848,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/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(2887,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)],[848]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_Power_Opower__class_Opower @ B @ ( c_Suc @ C ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(2074,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(1490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(651,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(2438,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(730,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(2615,plain,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(1917,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)],[415]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(2170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ C ) @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(612,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(2351,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(893,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(2993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(535,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(2191,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ A @ E @ F @ G @ H @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(1812,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(2177,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)],[528]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(2655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omin @ ( 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)],[747]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omin @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3049,plain,
$false,
inference(e,[status(thm)],[2163,2822,1411,2612,1823,2778,2072,1559,1237,1031,1899,1179,1818,1110,2199,1322,2295,2306,2341,2336,3008,1315,2595,2499,2427,962,1686,2250,1750,1924,2381,1618,2953,1073,1205,2854,1692,1305,1041,1200,2077,2117,2104,2808,1522,2776,1808,2671,1544,2014,2837,1142,1671,2740,3044,2448,2434,2168,1640,1954,1458,1497,2195,3017,1788,1426,1756,1310,1867,2184,1999,2316,1919,1988,2459,2901,945,1746,1835,2216,1576,1441,2082,1518,2531,2869,1887,2432,1914,2763,2548,2010,1935,1724,1475,2825,1967,1228,1623,1482,1254,1628,1709,2328,2039,2269,2755,1871,1455,2488,1992,1059,1055,1409,2735,2814,1985,1264,2217,2745,2571,2420,1892,2857,1087,1147,2049,1704,2767,1609,1568,2520,2158,2301,2852,1847,1922,2691,2373,1347,1572,1115,2929,2989,1362,2222,1373,1911,2650,2122,1978,1383,966,1946,1465,1664,2794,2324,1714,2027,2893,1632,2469,1418,2451,2236,1682,1136,1677,2540,2034,1960,2555,2058,1169,1447,2523,2137,998,1405,2965,1600,2205,2982,2762,2367,1928,2833,2281,2424,2371,1394,2772,1345,988,2639,1104,1697,1242,1651,2574,2646,2047,2232,2641,1604,2922,1470,2093,1783,2737,1067,2496,2660,1768,2061,1636,1730,3037,1057,1163,2589,2409,1091,2601,1021,2541,1580,1217,1666,1487,2606,2032,2528,2396,1274,2441,2673,957,1223,1343,2805,1570,1174,3022,1502,2150,1370,2414,2132,2890,2958,2445,1687,2068,974,1012,2653,2464,1938,1837,1602,2663,1555,2820,2872,1951,1210,1656,1079,1027,2327,3028,2345,1195,2211,1407,1128,2492,1634,2228,2112,1291,1402,1983,2115,948,1804,2577,980,2694,2726,1118,2268,2245,1350,1089,1234,1762,2515,1270,1772,1259,2990,1794,1953,2685,2841,1328,2359,1375,2709,1970,1096,2509,1540,1006,1138,2724,1719,2537,3018,1397,1082,1659,3000,2561,2830,1739,1075,1584,2613,2108,1889,2781,1493,2798,1160,2877,1424,2312,3010,2240,1842,2172,1810,1791,1214,2349,2551,1016,1207,1612,970,1150,2304,1131,1668,1050,2505,2006,1874,3005,2140,1525,1825,2968,1324,2285,1588,1099,985,2536,1297,1530,1539,1266,2387,1231,2153,2900,1552,2243,2355,1192,2566,1799,1002,1852,1429,2862,1759,1393,1333,1318,2926,2546,2208,1695,1712,2402,2089,2617,953,1732,2634,2749,1434,1857,1202,2203,1814,938,2883,921,2963,1286,1035,2368,1187,2915,1895,1167,2189,2995,2338,1996,926,2909,2121,1278,2001,1764,2176,2292,2391,2253,3042,2941,1548,2376,2260,2936,2729,1727,1510,2717,1219,1595,2734,1154,1833,2859,1884,1615,2791,2525,1620,2016,1388,1535,1701,1965,1520,2789,1125,2393,1752,2161,1786,2220,2293,1312,1865,3002,1239,2759,2166,2425,2474,1638,2891,2308,2457,1897,919,2557,1356,2573,2148,2346,2079,2538,2987,1574,2774,2955,1542,1144,1043,2802,1122,1439,2197,2721,2119,1282,2478,2084,2214,2383,2637,2422,2906,1048,2257,1933,2943,2945,1690,2896,2180,2182,1877,2742,1557,1630,1862,3034,1029,2874,943,2974,932,2025,2632,1339,2610,2314,2129,2343,2446,2757,1460,2289,2278,2553,1177,1381,2911,1820,1112,1688,1198,1699,2835,2086,1643,2064,2931,2022,1477,2101,2999,1562,2770,2418,1926,2365,2051,2765,1245,2481,1528,2620,2244,1000,2752,1364,1250,2984,1973,1805,1413,2054,2096,2665,1467,2471,2037,1684,1134,2629,1990,1472,2899,2582,3031,2816,2318,2271,1905,1420,2124,2234,2333,2846,2597,1958,968,1181,2513,1748,2298,1770,1025,2977,2012,1647,1780,2882,1516,1598,1225,1743,1400,1941,1252,2678,2518,1753,2407,2386,2850,1484,2831,993,2689,2747,2569,2454,1432,2920,1038,1869,2429,1262,1830,1901,1679,2044,3041,1336,1300,1452,2276,1980,1085,2322,2701,2486,2599,2903,2948,2411,2379,2543,1284,2579,2939,2848,2584,991,2675,2056,1358,2247,1543,1766,1849,1257,2838,2558,1802,1023,1353,2357,1955,2843,2145,2320,1052,2711,1585,2511,1094,978,1140,1797,3024,1717,2030,1881,1272,2924,1839,2088,2818,2885,2696,1157,2194,1654,2325,2658,1734,2626,1649,2352,1949,2828,2310,1844,2743,2997,2490,2187,1189,2110,1390,2226,2643,1108,3039,1326,2707,2273,1674,2290,1101,2811,2971,1854,2608,1822,2416,1276,2591,1590,1646,2443,1385,2594,1721,2174,2283,2389,1341,2098,1903,2135,1062,1508,995,2934,2152,2262,2796,2330,1308,2066,1706,2680,1607,1513,1661,2230,1994,2019,1045,2475,2786,2399,2041,2648,1777,1294,2462,1077,2362,2494,1444,2917,2623,2218,2287,1774,2683,1280,1578,2719,2233,1546,1625,2951,1248,1908,2003,2142,2155,2534,2255,950,2587,1593,2604,2008,1303,2768,1480,3015,2800,2201,2186,2070,2704,1172,2714,1065,955,2651,2783,1436,1859,1816,1495,1033,2961,1288,1710,2913,2091,2404,2223,960,2668,1165,1742,928,1930,2731,1152,1532,1537,1378,2467,2507,1505,1120,2502,2127,3025,1827,1582,2265,1019,1976,1550,1500,3020,2687,2864,982,1004,2484,2699,3013,2879,1320,1962,2563,2866,2436,1416,2106,3047,1069,2980,1331,1606,1653,1944,1367,940,935,1009,923,1737,2887,1184,2074,1463,1565,1490,2438,2238,2615,1917,2170,2351,2993,2191,1449,1812,2177,2655,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.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 16:47:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.18 % [INFO] Parsing done (285ms).
% 1.97/1.19 % [INFO] Running in sequential loop mode.
% 2.46/1.41 % [INFO] eprover registered as external prover.
% 2.46/1.41 % [INFO] cvc4 registered as external prover.
% 2.46/1.42 % [INFO] Scanning for conjecture ...
% 2.92/1.55 % [INFO] Found a conjecture and 919 axioms. Running axiom selection ...
% 3.66/1.72 % [INFO] Axiom selection finished. Selected 917 axioms (removed 2 axioms).
% 4.50/1.94 % [INFO] Problem is propositional (TPTP CNF).
% 4.50/1.96 % [INFO] Type checking passed.
% 4.50/1.97 % [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 ...
% 14.59/4.37 % External prover 'e' found a proof!
% 14.59/4.37 % [INFO] Killing All external provers ...
% 14.59/4.37 % Time passed: 3818ms (effective reasoning time: 3180ms)
% 14.59/4.37 % 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)>
% 14.59/4.38 % Axioms used in derivation (917): cls_type_Orecs_I2_J_0, cls_mult__eq__1__iff_1, cls_Suc__pred_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_add__0__left_0, cls_MI1_0, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_nat_Oinduct_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_min__max_Oinf__commute_0, cls_shift__commute_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_min__max_Ole__infE_0, cls_eq__add__iff2_1, cls_apps__eq__Abs__conv_0, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_mult__cancel2_0, cls_add__is__1_1, cls_less__diff__iff_1, cls_mult__zero__right_0, cls_of__nat__add_0, cls_gb__semiring_Omul__0_0, cls_Suc__inject_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_le__diff__iff_0, cls_gb__semiring_Osemiring__rules_I12_J_0, cls_of__nat__0_0, cls_gb__semiring_Osemiring__rules_I7_J_0, cls_min__max_Osup__inf__distrib1_0, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_lift_Osimps_I2_J_0, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_subst__App_0, cls_order__less__le__trans_0, cls_nat__0__less__mult__iff_1, cls_min__add__distrib__left_0, cls_Cons__eq__append__conv_5, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_subst__eq_0, cls_le__diff__conv_1, cls_left__add__mult__distrib_0, cls_xt1_I12_J_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_append__self__conv_0, cls_min__max_Oinf__sup__distrib1_0, cls_one__is__add_4, cls_min__max_Ole__sup__iff_2, cls_min__max_Oinf__le1_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_min__less__iff__conj_0, cls_mult__less__cancel__left__disj_1, cls_mult__is__0_2, cls_upt_Oinduct_1, cls_nat_Osplit_1, cls_type_Osimps_I3_J_0, cls_dB_Osimps_I8_J_0, cls_sum__squares__eq__zero__iff_0, cls_typing__elims_I3_J_0, cls_subject__reduction_0, cls_Suc__n__not__n_0, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_eq__diff__iff_0, cls_gb__semiring_Opwr__pwr_0, cls_add__is__1_2, cls_zero__le__mult__iff_3, cls_less__antisym_0, cls_one__le__mult__iff_0, cls_less__add__Suc2_0, cls_min__max_Osup__inf__absorb_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_list_Oinject_0, cls_add__increasing2_0, cls_min__0R_0, cls_replicate__empty_0, cls_linorder__neqE_0, cls_listsum_Osimps_I1_J_0, cls_add__strict__right__mono_0, cls_uT_H_0, cls_of__nat__less__iff_0, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, cls_MI2_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_nat__rec__Suc_0, cls_termination__basic__simps_I1_J_0, cls_add__le__cancel__left_1, cls_uIT_0, cls_gb__semiring_Osemiring__rules_I3_J_0, cls_type_Osimps_I4_J_0, cls_min__less__iff__disj_2, cls_not__less__eq_1, cls_appR_0, clsarity_nat__Orderings_Olinorder, cls_gb__semiring_Opwr__Suc_0, cls_add__is__0_0, cls_not__Cons__self2_0, cls_class__semiring_Osemiring__rules_I10_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_app__Var__IT_0, cls_nat__eq__add__iff1_0, cls_less__Suc__eq_2, cls_nat__add__left__cancel__less_0, cls_min__less__iff__disj_0, cls_one__is__add_1, cls_mult__nonpos__nonneg_0, cls_add__le__cancel__right_1, cls_gb__semiring_Osemiring__rules_I28_J_0, cls_nat_Osplit__asm_1, cls_class__ringb_Onoteq__reduce_0, cls_add__leE_0, cls_mult__less__imp__less__right_0, cls_order__less__trans_0, cls_nat__less__add__iff1_0, cls_of__nat__0__less__iff_0, cls_type_Osplit__asm_1, cls_mult__nonpos__nonpos_0, cls_min__max_Oinf__sup__distrib2_0, cls_comm__monoid__add_Omult__1__right_0, cls_drop__0_0, cls_nat__eq__add__iff2_0, cls_sum__squares__ge__zero_0, cls_add__diff__assoc2_0, cls_append__eq__Cons__conv_4, cls_add__nonpos__neg_0, cls_le__maxI2_0, cls_Suc__mult__cancel1_0, cls_char__size_0, cls_eq__Nil__appendI_0, cls_comm__monoid__add_Omult__assoc_0, cls_self__append__conv_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_add__cancel__21_1, cls_same__append__eq_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_mult__le__cancel__left__pos_0, cls_gb__semiring_Osemiring__rules_I13_J_0, cls_natgb_Oadd__mul__solve_0, cls_mult__less__cancel1_0, cls_le__0__eq_0, cls_mult__less__imp__less__left_0, cls_sum__squares__le__zero__iff_1, cls_listsum__append_0, cls_dB_Osimps_I7_J_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_mult__less__cancel2_1, cls_subst__preserves__beta_0, cls_less__max__iff__disj_2, cls_Abs_0, cls_mult__Suc__right_0, cls_add__nonneg__pos_0, cls_beta_0, cls_split__mult__neg__le_0, cls_append__Cons_0, cls_nat__less__add__iff2_1, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_nat__diff__add__eq1_0, cls_gr0I_0, cls_infinite__descent0_0, cls_lift__type_0, cls_add__gr__0_0, cls_mult__less__cancel__right__disj_3, cls_eq__add__iff1_0, cls_foldl__foldr1_0, cls_mult__eq__0__iff_0, cls_add__is__0_1, cls_less__max__iff__disj_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_lem0_0, cls_replicate__eq__replicate_0, cls_gb__semiring_Oadd__c_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_foldr_Osimps_I1_J_0, cls_diff__diff__right_0, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_min__max_Oless__infI2_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_add__le__mono_0, cls_diff__diff__cancel_0, cls_mult__left__mono__neg_0, cls_nat__minus__add__max_0, cls_ex__least__nat__le_0, cls_add__less__mono_0, cls_gb__semiring_Omul__c_0, cls_n__less__n__mult__m_0, cls_nat__less__cases_0, cls_mult__mono_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_append__eq__append__conv2_4, cls_nat__mult__eq__cancel1_0, cls_diff__diff__left_0, cls_class__semiring_Omul__0_0, cls_Var__apps__eq__Var__apps__conv_0, cls_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_infinite__descent0_1, cls_order__less__asym_0, cls_min__max_Ole__inf__iff_1, cls_class__semiring_Osemiring__rules_I7_J_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_less__add__iff2_0, cls_of__nat__le__iff_1, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_append1__eq__conv_1, cls_less__iff__diff__less__0_1, cls_headT_0, cls_listsum_Osimps_I2_J_0, cls_zero__le__mult__iff_0, cls_mult__strict__mono_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_mult__left__mono_0, cls_of__nat__le__iff_0, cls_gb__semiring_Omul__d_0, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, cls_mult__pos__neg_0, cls_nat__0__less__mult__iff_0, cls_order__eq__refl_0, cls_shift__eq_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_mult__eq__1__iff_0, cls_nat__gcd_Osimps_0, cls_mult__strict__right__mono_0, clsarity_fun__Orderings_Obot, cls_one__le__mult__iff_2, cls_linorder__antisym__conv2_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_min__max_Ole__infE_1, cls_gb__semiring_Osemiring__rules_I16_J_0, cls_gb__semiring_Osemiring__rules_I14_J_0, cls_foldl__absorb0_0, cls_Suc__leI_0, cls_add__Suc_0, cls_power__Suc2_0, cls_drop__Suc__Cons_0, cls_le__imp__diff__is__add_1, cls_dB_Osimps_I3_J_0, cls_mult__le__cancel1_1, cls_replicate__append__same_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_max__0R_0, cls_bot__least_0, cls_subst__Var_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_diff__add__inverse2_0, cls_xt1_I10_J_0, cls_le__maxI1_0, cls_append__Nil2_0, cls_mult__less__cancel2_2, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_append__self__conv2_0, cls_nat_Oinducts_0, cls_one__is__add_5, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_min__max_Odistrib__inf__le_0, cls_diff__mult__distrib2_0, cls_bot__nat__def_0, cls_Nil__is__append__conv_0, cls_add__left__mono_0, cls_mult__is__0_1, cls_add__nonneg__eq__0__iff_0, cls_add__less__cancel__right_1, cls_nat_Osplit_0, cls_Var__apps__eq__Var__apps__conv_1, cls_not__less__iff__gr__or__eq_0, cls_typing__elims_I2_J_0, cls_diff__Suc__Suc_0, cls_min__max_Ole__supE_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_min__max_Osup__least_0, cls_no__zero__divisors_0, cls_zero__le__mult__iff_4, cls_typing__elims_I3_J_1, cls_mult__le__mono_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_min__max_Ole__sup__iff_1, cls_max__diff__distrib__left_0, cls_gb__semiring_Osemiring__rules_I9_J_0, cls_gb__semiring_Omul__1_0, cls_add__strict__left__mono_0, cls_of__nat__0__le__iff_0, cls_le__iff__diff__le__0_0, cls_mult__neg__pos_0, cls_less__add__iff1_0, cls_nat__diff__split_0, 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cls_add__eq__self__zero_0, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_power__less__imp__less__base_0, cls_add__mono_0, cls_n__not__Suc__n_0, cls_le__max__iff__disj_0, cls_type__induct_2, cls_min__le__iff__disj_1, cls_sum__squares__gt__zero__iff_0, cls_gb__semiring_Osemiring__rules_I24_J_0, cls_min__diff__distrib__left_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_add__neg__nonpos_0, cls_foldl__append_0, cls_Suc__leD_0, clsarity_fun__Orderings_Opreorder, cls_min__le__iff__disj_2, cls_mult__right__less__imp__less_0, cls_nat__less__add__iff1_1, cls_power__inject__base_0, cls_min__max_Ole__infI_0, cls_nat__le__add__iff1_1, cls_less__SucI_0, cls_nat__mult__le__cancel1_0, cls_not__less0_0, cls_nat__mult__assoc_0, cls_diffs0__imp__equal_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_min__max_Ole__iff__inf_0, cls_class__ringb_Osubr0__iff_1, cls_shift__gt_0, cls_one__is__add_3, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_Nil__is__append__conv_2, cls_nat__0__less__mult__iff_2, cls_append__replicate__commute_0, cls_mult__less__cancel__left__disj_2, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_gb__semiring_Osemiring__rules_I19_J_0, cls_class__semiring_Opwr__mul_0, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_replicate__empty_1, cls_subst__Var__IT_0, cls_gb__semiring_Omul__a_0, cls_type__induct_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_min__max_Ole__iff__sup_0, cls_less__max__iff__disj_1, cls_Suc__less__eq_0, cls_list__app__typeE_0, cls_zero__le__power_0, cls_gb__semiring_Osemiring__rules_I20_J_0, cls_max__less__iff__conj_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_nat__case__Suc_0, cls_order__less__imp__le_0, cls_add__leE_1, cls_mult__cancel1_0, cls_max__add__distrib__left_0, cls_gb__semiring_Opwr__0_0, cls_foldl__Nil_0, cls_abs__typeE_0, cls_le__eqI_1, cls_Lambda_0, cls_Suc__diff__le_0, cls_gb__semiring_Osemiring__rules_I4_J_0, cls_mult__eq__0__iff_1, cls_nat__case__0_0, cls_le__iff__diff__le__0_1, cls_add__gr__0_2, cls_diff__le__mono_0, cls_type_Osplit__asm_0, cls_add__less__le__mono_0, cls_lift_Osimps_I1_J_0, cls_min__max_Ole__supI2_0, cls_add__gr__0_1, cls_min__max_Ole__supE_1, cls_diff__commute_0, cls_le__add1_0, cls_type__induct_1, cls_upt_Oinduct_0, cls_le__less__Suc__eq_1, cls_less__Suc0_1, cls_subst__lift_0, cls_termination__basic__simps_I2_J_0, cls_class__ringb_Osubr0__iff_0, cls_le__eq__less__or__eq_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_class__semiring_Omul__pwr_0, cls_eq__iff__diff__eq__0_0, cls_gb__semiring_Opwr__mul_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_mult__idem_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, clsarity_nat__Orderings_Oorder, cls_appL_0, cls_mult__le__less__imp__less_0, cls_empty__replicate_1, cls_list_Osimps_I2_J_0, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_gb__semiring_Osemiring__rules_I11_J_0, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, cls_T_0, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_mult__less__cancel__left__neg_0, cls_zero__less__Suc_0, cls_append1__eq__conv_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_0, cls_min__diff_0, cls_Beta_0, cls_natgb_Oadd__mul__solve_1, cls_min__max_Osup__commute_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_nat__OrderedGroup_Osemigroup__add, cls_max__Suc__Suc_0, cls_gb__semiring_Osemiring__rules_I23_J_0, cls_less__eqI_1, cls_dB_Osimps_I9_J_0, cls_zero__le__imp__of__nat_0, cls_not__less__eq__eq_0, cls_sum__squares__le__zero__iff_0, cls_ex__least__nat__le_1, cls_add__le__cancel__right_0, cls_gb__semiring_Osemiring__rules_I1_J_0, cls_mult__eq__1__iff_2, cls_mult__less__cancel__left__pos_0, cls_nat__add__commute_0, cls_split__mult__neg__le_1, cls_nat__eq__add__iff2_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_argsT_0, cls_add__diff__inverse_0, cls_power__mono_0, cls_of__nat__less__0__iff_0, cls_type_Osimps_I6_J_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_le__refl_0, cls_min__less__iff__disj_1, cls_nat_Oinduct_1, cls_min__0L_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_gb__semiring_Osemiring__rules_I15_J_0, cls_power__0__left_1, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_nat_Osize_I1_J_0, cls_zero__le__mult__iff_2
% 14.59/4.38 % No. of inferences in proof: 1837
% 14.59/4.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3818 ms resp. 3180 ms w/o parsing
% 15.91/4.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.91/4.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------