TSTP Solution File: LCL755-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:31:26 EDT 2023
% Result : Unsatisfiable 10.46s 3.32s
% Output : Refutation 11.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 816
% Syntax : Number of formulae : 1569 ( 295 unt; 64 typ; 0 def)
% Number of atoms : 3715 ( 908 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 20762 (2100 ~;2210 |; 0 &;16452 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 64 usr; 5 con; 0-3 aty)
% Number of variables : 4216 ( 0 ^;4216 !; 0 ?;4216 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i > $o ).
thf(v_ra_type,type,
v_ra: $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(v_ia_type,type,
v_ia: $i ).
thf(v_ja_type,type,
v_ja: $i ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
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_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_Orderings_Oord__class_Omax_type,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(c_Orderings_Oord__class_Omin_type,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(class_Divides_Osemiring__div_type,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_type,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_Divides_Oring__div_type,type,
class_Divides_Oring__div: $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(610,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2163,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(243,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(1322,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)],[243]) ).
thf(320,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(1501,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(1024,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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)],[119]) ).
thf(263,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(1369,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)],[263]) ).
thf(675,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(2306,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)],[675]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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_comm__semiring__class_Odistrib_0) ).
thf(1767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[436]) ).
thf(208,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(1237,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)],[208]) ).
thf(61,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(893,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)],[61]) ).
thf(470,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(1850,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)],[470]) ).
thf(81,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(941,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)],[81]) ).
thf(183,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(1179,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)],[183]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(233,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(1295,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)],[233]) ).
thf(662,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(2280,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(648,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(2250,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)],[648]) ).
thf(483,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(1879,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)],[483]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1337,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(415,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(1718,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)],[415]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(2094,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ A @ C ) )
| ~ ( c_Lambda_Obeta @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(282,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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(1411,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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(2336,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ A ) @ B @ C )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(595,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(2131,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)],[595]) ).
thf(533,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(1995,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)],[533]) ).
thf(653,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(2263,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)],[653]) ).
thf(746,axiom,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(2480,plain,
! [A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ A ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(90,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(962,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)],[90]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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(1982,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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)],[527]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(1750,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ A @ B ) @ ( c_Lambda_OdB_OApp @ C @ B ) )
| ~ ( c_Lambda_Obeta @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(174,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(1158,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)],[174]) ).
thf(581,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(2104,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)],[581]) ).
thf(485,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(1882,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)],[485]) ).
thf(138,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(1068,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)],[138]) ).
thf(331,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(1522,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(562,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(2062,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)],[562]) ).
thf(106,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(994,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)],[106]) ).
thf(140,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(1073,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)],[140]) ).
thf(541,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(2014,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)],[541]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(1728,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(314,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(1486,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)],[314]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__if_1) ).
thf(1200,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(569,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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_class__semiring_Osemiring__rules_I8_J_0) ).
thf(2077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[569]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(1924,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(631,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(2210,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)],[631]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(647,axiom,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(2248,plain,
! [A: $i] :
( ( c_Divides_Odiv__class_Omod @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(2114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(167,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(1142,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)],[167]) ).
thf(55,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(705,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(2380,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)],[705]) ).
thf(523,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(1971,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)],[523]) ).
thf(446,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(1793,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)],[446]) ).
thf(395,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_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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_class__semiring_Omul__d_0) ).
thf(1671,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_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[395]) ).
thf(388,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(1655,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)],[388]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(1137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(550,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(2035,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)],[550]) ).
thf(422,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(1735,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)],[422]) ).
thf(732,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(2448,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(479,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(1872,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)],[479]) ).
thf(206,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(1233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ 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_add__gr__0_1) ).
thf(1458,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ 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)],[301]) ).
thf(318,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(1497,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(625,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(2195,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ 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(1078,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ 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)],[142]) ).
thf(444,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(1788,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)],[444]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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(1867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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)],[477]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(2184,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(177,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(1164,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)],[177]) ).
thf(20,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(797,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)],[20]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ 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(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(600,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(2141,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)],[600]) ).
thf(503,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(1919,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)],[503]) ).
thf(737,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(2459,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)],[737]) ).
thf(252,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(1342,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)],[252]) ).
thf(70,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(913,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)],[70]) ).
thf(323,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(1507,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(698,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(2360,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(34,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(829,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)],[34]) ).
thf(634,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(2216,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)],[634]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(1001,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(555,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(2046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ B @ A )
= ( c_Divides_Odiv__class_Omod @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(501,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(1914,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)],[501]) ).
thf(751,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(2491,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(544,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(2020,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)],[544]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(973,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(385,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(1650,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)],[385]) ).
thf(259,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(1359,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)],[259]) ).
thf(571,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(2082,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)],[571]) ).
thf(615,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(2173,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)],[615]) ).
thf(334,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 @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(1529,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 @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(407,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(1703,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)],[407]) ).
thf(714,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(2405,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(427,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(1746,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)],[427]) ).
thf(64,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(898,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)],[64]) ).
thf(638,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(2227,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)],[638]) ).
thf(354,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(1576,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)],[354]) ).
thf(204,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(1228,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)],[204]) ).
thf(312,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( 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 ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(1482,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( 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 ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(684,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(2328,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)],[684]) ).
thf(552,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(2039,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)],[552]) ).
thf(656,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(2269,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)],[656]) ).
thf(497,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(1907,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)],[497]) ).
thf(659,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(2274,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)],[659]) ).
thf(300,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(1455,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(750,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(2488,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(188,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(1191,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)],[188]) ).
thf(163,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(1132,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)],[163]) ).
thf(84,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(949,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)],[84]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ B ) @ ( c_Suc @ C ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ C ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ B ) @ ( c_Suc @ C ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ A @ C ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(281,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(1409,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)],[281]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( 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(1760,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(234,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(1298,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)],[234]) ).
thf(247,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(1330,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)],[247]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ 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_add__le__mono_0) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ 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)],[220]) ).
thf(341,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(1545,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)],[341]) ).
thf(490,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(1892,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)],[490]) ).
thf(613,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(2169,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(94,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(969,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)],[94]) ).
thf(351,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(1568,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)],[351]) ).
thf(608,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(1641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(438,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ ( 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(1773,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ ( c_Suc @ B ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(260,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(1362,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)],[260]) ).
thf(481,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(1875,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)],[481]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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_add__mult__distrib2_0) ).
thf(1922,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[504]) ).
thf(29,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(817,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)],[29]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(556,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(2049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(408,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(1704,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)],[408]) ).
thf(489,axiom,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(1890,plain,
! [A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(114,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(1013,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)],[114]) ).
thf(9,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(770,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)],[9]) ).
thf(276,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ 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(1398,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ 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)],[276]) ).
thf(56,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(881,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)],[56]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(1815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(317,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(1494,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(617,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(2178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ 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(1489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ tc_nat ) )
| ( C = D )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ 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(1664,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
| ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(499,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 @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(1911,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 @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(249,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(1334,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)],[249]) ).
thf(461,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(1828,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(23,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(806,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(92,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(966,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(67,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(905,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)],[67]) ).
thf(736,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(2456,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(538,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(2007,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)],[538]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(304,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(1465,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(682,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(2324,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(1714,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(126,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(1040,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)],[126]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(1109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(377,axiom,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(1632,plain,
! [A: $i] :
( A
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(742,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(2469,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)],[742]) ).
thf(734,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(2451,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)],[734]) ).
thf(642,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(2236,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(399,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(1682,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)],[399]) ).
thf(36,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(834,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(474,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(1858,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)],[474]) ).
thf(476,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(1864,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)],[476]) ).
thf(185,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(1183,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)],[185]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(567,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(2073,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)],[567]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(663,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(2281,plain,
! [A: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) )
| ~ ( c_InductTermi_OIT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(274,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(1394,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ 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(1433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(2154,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(404,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(1696,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)],[404]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
thf(1564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(467,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(1843,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(560,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(2058,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)],[560]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(1896,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(54,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(877,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(1447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(49,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(866,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(487,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(1886,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)],[487]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(1119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(373,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(1622,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)],[373]) ).
thf(722,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(2424,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)],[722]) ).
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(774,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(702,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(2371,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(536,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(2002,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(108,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(645,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(2242,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(103,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(988,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)],[103]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ 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__double__add__iff__zero__less__single__add_1) ).
thf(1104,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(210,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(1242,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(43,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(849,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)],[43]) ).
thf(386,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(1651,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)],[386]) ).
thf(74,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(925,plain,
class_OrderedGroup_Omonoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(588,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2118,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(172,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(1153,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)],[172]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
thf(1470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(410,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(1708,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)],[410]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(1311,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(640,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(2232,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)],[640]) ).
thf(670,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(2296,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ 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_add__nonneg__nonneg_0) ).
thf(2000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ 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)],[535]) ).
thf(379,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(1636,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(129,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 )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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_add__nonneg__eq__0__iff_2) ).
thf(1047,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 )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[129]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
thf(1730,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(729,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(2441,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)],[729]) ).
thf(148,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(1091,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)],[148]) ).
thf(724,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(2428,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)],[724]) ).
thf(32,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(825,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(329,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(1519,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)],[329]) ).
thf(356,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(1580,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)],[356]) ).
thf(216,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(1255,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)],[216]) ).
thf(199,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(1217,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)],[199]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ 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(1666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( D = E )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(2032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(2396,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ A ) @ B )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(347,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(1560,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)],[347]) ).
thf(271,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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 )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(1387,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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 )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(127,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(1042,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)],[127]) ).
thf(85,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(952,plain,
class_Divides_Osemiring__div @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ D @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(1676,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= A )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(596,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(2133,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(372,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(1619,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_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(604,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(2150,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)],[604]) ).
thf(71,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(916,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)],[71]) ).
thf(510,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(1938,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)],[510]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(1968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(345,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(1555,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)],[345]) ).
thf(488,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(1888,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( 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(1687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( 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)],[401]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(2200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(683,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(2327,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)],[683]) ).
thf(752,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(2492,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)],[752]) ).
thf(227,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(1281,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)],[227]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ 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(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(353,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(1573,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)],[353]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ D @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ D @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(123,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ 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_Suc__pred_H_0) ).
thf(1032,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ 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)],[123]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( 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_eq__add__iff2_0) ).
thf(1602,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
| ( D
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[365]) ).
thf(726,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(2433,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)],[726]) ).
thf(745,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(2477,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(565,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
thf(2068,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(458,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(1819,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)],[458]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(1624,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(618,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2181,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(4,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(757,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(691,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(2345,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(1195,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(280,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(1407,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)],[280]) ).
thf(378,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(1634,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)],[378]) ).
thf(273,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(1392,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)],[273]) ).
thf(278,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(1402,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)],[278]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(2100,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(704,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(2377,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)],[704]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
thf(1804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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_mod__mult__distrib2_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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)],[246]) ).
thf(136,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(1064,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)],[136]) ).
thf(156,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(1111,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)],[156]) ).
thf(473,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(1856,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)],[473]) ).
thf(99,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(980,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(287,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(1425,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)],[287]) ).
thf(150,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(1096,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)],[150]) ).
thf(51,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(869,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)],[51]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(361,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(1592,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)],[361]) ).
thf(672,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(2300,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)],[672]) ).
thf(147,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(1089,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)],[147]) ).
thf(339,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(1541,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)],[339]) ).
thf(223,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(1270,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)],[223]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ 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(1017,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(338,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(1540,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(175,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1160,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1,negated_conjecture,
c_InductTermi_OIT @ v_ra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(753,plain,
c_InductTermi_OIT @ v_ra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(1739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(677,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(2312,plain,
! [B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(2080,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(644,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(2240,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)],[644]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(2108,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(195,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(1207,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)],[195]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(369,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(1612,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)],[369]) ).
thf(285,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(1419,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)],[285]) ).
thf(121,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(1028,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)],[121]) ).
thf(144,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 @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1082,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 @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(1964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(512,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( 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 ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1942,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( 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 ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(65,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(901,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)],[65]) ).
thf(720,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(2419,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)],[720]) ).
thf(141,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(1075,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)],[141]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(1214,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(693,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(2349,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)],[693]) ).
thf(679,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(2317,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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(1744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( 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)],[426]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1776,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(269,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(1382,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)],[269]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(1799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(528,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(1984,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)],[528]) ).
thf(471,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(1852,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)],[471]) ).
thf(480,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(1874,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(289,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(1429,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)],[289]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ 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(1720,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(1979,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(244,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(1324,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)],[244]) ).
thf(665,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(2285,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(592,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(2125,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)],[592]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(298,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(1451,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)],[298]) ).
thf(674,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(2304,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(221,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(1266,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)],[221]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(1231,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(696,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( 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_one__is__add_5) ).
thf(2355,plain,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[696]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(740,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(2465,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)],[740]) ).
thf(134,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(1060,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)],[134]) ).
thf(557,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(2052,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)],[557]) ).
thf(747,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(2482,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)],[747]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(1599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Otimes__class_Otimes @ B @ E @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ D @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(531,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(1991,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(628,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(2203,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)],[628]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(440,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(1779,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)],[440]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(2208,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(713,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(2402,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)],[713]) ).
thf(327,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(1515,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)],[327]) ).
thf(120,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(1026,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)],[120]) ).
thf(371,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(1616,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ A @ tc_nat )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(86,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(953,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)],[86]) ).
thf(59,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(888,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)],[59]) ).
thf(75,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(926,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)],[75]) ).
thf(412,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(1712,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)],[412]) ).
thf(468,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(1846,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)],[468]) ).
thf(229,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(1286,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)],[229]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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_one__is__add_2) ).
thf(2368,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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)],[701]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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_one__is__add_0) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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)],[716]) ).
thf(574,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(2089,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)],[574]) ).
thf(10,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(773,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
!= ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(688,axiom,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(2338,plain,
! [A: $i] :
( ( c_Suc @ A )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(590,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(2121,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)],[590]) ).
thf(226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(1278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ D @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ E @ C @ A )
!= ( c_Divides_Odiv__class_Omod @ F @ C @ A ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ E @ B @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ F @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(384,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(1648,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)],[384]) ).
thf(91,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(965,plain,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(718,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(2413,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)],[718]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(2391,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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)],[709]) ).
thf(519,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(1959,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)],[519]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ( 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(2253,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(200,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
thf(1219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(1927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(265,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(1374,plain,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(652,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(2260,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(1146,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(1754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(668,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(2292,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)],[668]) ).
thf(547,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(2028,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)],[547]) ).
thf(362,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(1595,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)],[362]) ).
thf(30,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(819,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)],[30]) ).
thf(66,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(904,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat )
| ( C
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
thf(1833,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ A @ D @ tc_nat )
| ( C
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(1916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(486,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(1884,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)],[486]) ).
thf(442,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(1784,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)],[442]) ).
thf(622,axiom,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ 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__diff__1_0) ).
thf(2188,plain,
! [A: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ 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)],[622]) ).
thf(430,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(1752,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)],[430]) ).
thf(542,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(2016,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)],[542]) ).
thf(33,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(826,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)],[33]) ).
thf(330,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ 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(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(203,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(1226,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)],[203]) ).
thf(597,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(2134,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)],[597]) ).
thf(447,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(1795,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)],[447]) ).
thf(406,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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(1701,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 @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(609,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(2161,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)],[609]) ).
thf(321,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(1503,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)],[321]) ).
thf(636,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(2220,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)],[636]) ).
thf(264,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(1371,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)],[264]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(133,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(1058,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)],[133]) ).
thf(248,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(1332,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)],[248]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ 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(1765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ 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)],[435]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(919,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( B
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(744,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(2474,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)],[744]) ).
thf(394,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(1669,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)],[394]) ).
thf(624,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(2193,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)],[624]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(1786,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(380,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(1638,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Oone__class_Oone @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(202,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(1224,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)],[202]) ).
thf(603,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(2148,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)],[603]) ).
thf(680,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(2319,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)],[680]) ).
thf(258,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(1356,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)],[258]) ).
thf(7,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(764,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)],[7]) ).
thf(491,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(1894,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)],[491]) ).
thf(15,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(784,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)],[15]) ).
thf(332,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(1524,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)],[332]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(2116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OApp @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(1690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(48,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(863,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)],[48]) ).
thf(196,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(1209,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)],[196]) ).
thf(589,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(2119,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)],[589]) ).
thf(572,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(2084,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)],[572]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ 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_add__gr__0_2) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ 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)],[633]) ).
thf(706,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ C ) @ ( c_Suc @ D ) ) @ ( c_Lambda_Osubst @ E @ B @ D ) @ C )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ E @ C ) @ B @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(2383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ ( c_Lambda_Olift @ B @ C ) @ ( c_Suc @ D ) ) @ ( c_Lambda_Osubst @ E @ B @ D ) @ C )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ A @ E @ C ) @ B @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(104,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(990,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)],[104]) ).
thf(107,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(996,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)],[107]) ).
thf(646,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(2246,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)],[646]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(417,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(1722,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)],[417]) ).
thf(168,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(1144,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(266,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(1376,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)],[266]) ).
thf(293,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(1439,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)],[293]) ).
thf(60,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(890,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)],[60]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ 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_mod__le__divisor_0) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ 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)],[482]) ).
thf(5,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(758,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)],[5]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(584,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(2111,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)],[584]) ).
thf(498,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(1909,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)],[498]) ).
thf(731,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(2446,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)],[731]) ).
thf(42,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(848,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(62,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(895,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(232,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(1293,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)],[232]) ).
thf(182,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(1177,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)],[182]) ).
thf(738,axiom,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( 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(2461,plain,
! [B: $i,A: $i] : ( c_Lambda_Obeta @ ( 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)],[738]) ).
thf(26,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(811,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(619,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(2182,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)],[619]) ).
thf(546,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(2025,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)],[546]) ).
thf(143,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(1080,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)],[143]) ).
thf(678,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(2314,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(594,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(2129,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)],[594]) ).
thf(690,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(2343,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)],[690]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ 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(1630,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ 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)],[376]) ).
thf(532,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(1993,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)],[532]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
thf(1460,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat ) )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(2289,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
= ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(118,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(1022,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)],[118]) ).
thf(77,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(932,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)],[77]) ).
thf(516,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(1952,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)],[516]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ B @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(2365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ B @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oplus__class_Oplus @ D @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(1474,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(405,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(1699,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)],[405]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(573,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(2086,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(13,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(780,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(157,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(1113,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)],[157]) ).
thf(545,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(2022,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)],[545]) ).
thf(310,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(1477,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)],[310]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(607,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(2156,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)],[607]) ).
thf(73,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(922,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)],[73]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(348,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(1562,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)],[348]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(983,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(568,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(2075,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)],[568]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
thf(1198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ C @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ A @ tc_nat ) @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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_mod__mult__distrib_0) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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)],[466]) ).
thf(275,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(632,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(2212,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)],[632]) ).
thf(89,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(959,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)],[89]) ).
thf(614,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(2171,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)],[614]) ).
thf(137,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(1066,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)],[137]) ).
thf(295,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(1445,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)],[295]) ).
thf(563,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(2064,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)],[563]) ).
thf(115,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(1015,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)],[115]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(558,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(2054,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)],[558]) ).
thf(357,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(1583,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)],[357]) ).
thf(453,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(1809,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)],[453]) ).
thf(178,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(1166,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)],[178]) ).
thf(193,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(1203,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)],[193]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(1467,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(657,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(2271,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)],[657]) ).
thf(743,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(2471,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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)],[743]) ).
thf(496,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(1905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(551,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(2037,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)],[551]) ).
thf(641,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(2234,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)],[641]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
= ( 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(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ A @ B ) @ C )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ 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 @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ 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 @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(754,plain,
! [B: $i,A: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(184,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(1181,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)],[184]) ).
thf(38,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(836,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)],[38]) ).
thf(537,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(2005,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)],[537]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(1413,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(391,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(1662,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)],[391]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(2096,plain,
! [B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ A @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(733,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(2449,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)],[733]) ).
thf(324,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(1509,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)],[324]) ).
thf(686,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(2333,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)],[686]) ).
thf(650,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(2256,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)],[650]) ).
thf(671,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(2298,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)],[671]) ).
thf(437,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(1770,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)],[437]) ).
thf(58,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(887,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(95,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(971,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(366,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(1605,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)],[366]) ).
thf(616,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(2175,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(335,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(1531,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)],[335]) ).
thf(313,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(1484,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)],[313]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(1098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(342,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(1547,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)],[342]) ).
thf(428,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(1748,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)],[428]) ).
thf(139,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(1070,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)],[139]) ).
thf(52,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(872,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)],[52]) ).
thf(703,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(2375,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)],[703]) ).
thf(173,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(1156,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)],[173]) ).
thf(561,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(2060,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)],[561]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
thf(1400,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ B @ tc_nat )
= ( c_Orderings_Oord__class_Omax @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(350,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(1566,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)],[350]) ).
thf(601,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
thf(2143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) ) @ B @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ C ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(715,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(2407,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)],[715]) ).
thf(707,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(2386,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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)],[707]) ).
thf(575,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(2092,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ 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(2165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) @ 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)],[611]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(125,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(1038,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)],[125]) ).
thf(478,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(1869,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)],[478]) ).
thf(660,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(2276,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OApp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ 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_mod__less__divisor_0) ).
thf(1901,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) @ 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)],[494]) ).
thf(25,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(808,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)],[25]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(1679,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(2044,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(131,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(1053,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)],[131]) ).
thf(319,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(1499,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)],[319]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(1790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(529,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(1987,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)],[529]) ).
thf(414,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(1716,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(455,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(1813,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)],[455]) ).
thf(235,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(1300,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)],[235]) ).
thf(187,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(1188,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)],[187]) ).
thf(186,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(1186,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)],[186]) ).
thf(219,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(1262,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)],[219]) ).
thf(207,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(1235,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ 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(1317,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ tc_nat )
= B )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(434,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1763,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(389,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(681,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( 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_add__is__1_5) ).
thf(2322,plain,
( ( c_HOL_Oplus__class_Oplus @ ( 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)],[681]) ).
thf(717,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) @ B )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(2411,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ A ) @ B )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ A @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(585,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(2113,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(723,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(2426,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(450,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(1802,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)],[450]) ).
thf(201,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(1221,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)],[201]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
thf(1427,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_nat ) @ C @ tc_nat ) @ D @ tc_nat ) @ E @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(1797,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(112,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(1008,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)],[112]) ).
thf(548,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(2030,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)],[548]) ).
thf(655,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ D ) @ ( c_Lambda_Olift @ B @ D ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ A @ B @ C ) @ D )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ D ) @ ( c_Lambda_Olift @ B @ D ) @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(209,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(1240,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)],[209]) ).
thf(559,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(2056,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)],[559]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(493,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(1898,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) )
| ~ ( c_lessequals @ C @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(469,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(1849,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(217,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(1257,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(661,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(2279,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)],[661]) ).
thf(697,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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_one__is__add_1) ).
thf(2357,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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)],[697]) ).
thf(517,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(1955,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)],[517]) ).
thf(602,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(2145,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)],[602]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ A @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(166,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(1140,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)],[166]) ).
thf(484,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1881,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(224,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(1272,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)],[224]) ).
thf(511,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(1940,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)],[511]) ).
thf(41,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(845,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)],[41]) ).
thf(465,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(1839,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)],[465]) ).
thf(400,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(1685,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)],[400]) ).
thf(515,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(1949,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(457,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(1817,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)],[457]) ).
thf(500,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(1913,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(692,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(2347,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)],[692]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(1517,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(1781,plain,
! [B: $i,A: $i] :
( ( A
!= ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(161,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(1126,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)],[161]) ).
thf(452,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(1807,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)],[452]) ).
thf(534,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(1998,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)],[534]) ).
thf(695,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(2352,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(145,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(1084,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)],[145]) ).
thf(676,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(2310,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(97,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(976,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)],[97]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( 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(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ C @ D @ tc_nat ) )
| ~ ( 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)],[113]) ).
thf(272,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(1390,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 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(230,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(1289,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)],[230]) ).
thf(299,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1453,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(360,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(1590,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)],[360]) ).
thf(245,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(1326,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)],[245]) ).
thf(215,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(1253,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)],[215]) ).
thf(27,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(813,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(396,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(1674,plain,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(135,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(1062,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 @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(472,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(1854,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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)],[472]) ).
thf(725,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(2431,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)],[725]) ).
thf(16,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(786,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)],[16]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(719,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(2416,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(605,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(2152,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(710,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(2394,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)],[710]) ).
thf(383,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(1646,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)],[383]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(2443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(612,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(2167,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)],[612]) ).
thf(658,axiom,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(2273,plain,
! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(664,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( 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_add__is__1_4) ).
thf(2283,plain,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( 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)],[664]) ).
thf(708,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(2389,plain,
! [B: $i,A: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(309,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(1476,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(63,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(896,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(578,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(2098,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)],[578]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ 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_pos__add__strict_0) ).
thf(1903,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ 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)],[495]) ).
thf(598,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(2135,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)],[598]) ).
thf(83,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(946,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)],[83]) ).
thf(152,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(1101,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)],[152]) ).
thf(211,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(1244,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(459,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(1822,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)],[459]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ D @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) @ D @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ( 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(2462,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OApp @ A @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(626,axiom,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(2198,plain,
! [A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(564,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(2066,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)],[564]) ).
thf(699,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(2362,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(197,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(1212,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)],[197]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(326,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(1513,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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)],[326]) ).
thf(390,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1661,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(35,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(832,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)],[35]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(1442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Oring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ B @ D @ A ) @ ( c_Divides_Odiv__class_Omod @ C @ D @ A ) @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(128,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(1045,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)],[128]) ).
thf(539,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(2009,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(475,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(1861,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)],[475]) ).
thf(712,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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_one__is__add_3) ).
thf(2399,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ A @ B @ 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)],[712]) ).
thf(553,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(2041,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)],[553]) ).
thf(76,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(929,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)],[76]) ).
thf(685,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(2330,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ A @ B @ tc_nat ) )
!= B )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ A ) @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(409,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(1706,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)],[409]) ).
thf(189,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(1193,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)],[189]) ).
thf(639,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(2230,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)],[639]) ).
thf(669,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(2294,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)],[669]) ).
thf(238,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(1309,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)],[238]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(1161,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( B
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_nat ) @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(370,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(1614,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)],[370]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(2421,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ C )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(21,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(800,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)],[21]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(666,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(580,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(2102,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)],[580]) ).
thf(325,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(1512,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(673,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(2302,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)],[673]) ).
thf(418,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(1725,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)],[418]) ).
thf(93,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(967,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(37,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(835,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(268,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(1380,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)],[268]) ).
thf(311,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(1480,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)],[311]) ).
thf(591,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(2123,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 ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(635,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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(2218,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( 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)],[635]) ).
thf(651,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(2258,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)],[651]) ).
thf(355,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 ) @ ( c_HOL_Oplus__class_Oplus @ 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_add__pos__pos_0) ).
thf(1578,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 ) @ ( c_HOL_Oplus__class_Oplus @ 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)],[355]) ).
thf(518,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(1957,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)],[518]) ).
thf(45,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(854,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)],[45]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( 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(1303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( 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)],[236]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
thf(1527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ C @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ B @ tc_nat ) @ E @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ A @ D @ tc_nat ) @ B @ tc_nat ) @ C @ tc_nat ) @ E @ tc_nat )
| ~ ( c_lessequals @ D @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(170,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(1148,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)],[170]) ).
thf(50,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ 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(867,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 @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(432,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(1757,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)],[432]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
!= ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(1989,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ C @ A @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(240,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(1314,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(621,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(2186,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)],[621]) ).
thf(24,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(807,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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_add__mult__distrib_0) ).
thf(1710,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ C @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[411]) ).
thf(637,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(2223,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)],[637]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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(2340,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( 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)],[689]) ).
thf(87,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(955,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(1742,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(403,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(1693,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)],[403]) ).
thf(566,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(2070,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)],[566]) ).
thf(180,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(1172,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)],[180]) ).
thf(8,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(767,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)],[8]) ).
thf(254,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(1346,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)],[254]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ 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(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oplus__class_Oplus @ B @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(593,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(2127,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)],[593]) ).
thf(256,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(1352,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 @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ 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_mod__lemma_0) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_Divides_Odiv__class_Omod @ B @ C @ tc_nat ) @ tc_nat ) @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ D @ A @ 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)],[222]) ).
thf(47,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(860,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)],[47]) ).
thf(267,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(1378,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)],[267]) ).
thf(741,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(2467,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)],[741]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(822,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(748,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(2484,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(322,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(1505,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(149,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(1093,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)],[149]) ).
thf(507,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ 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(1930,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(270,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(1384,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)],[270]) ).
thf(749,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(2485,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)],[749]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(654,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(2265,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)],[654]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(525,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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_double__eq__0__iff_1) ).
thf(1976,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[525]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(68,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(908,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)],[68]) ).
thf(105,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(992,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)],[105]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(290,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(1431,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)],[290]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(1004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Divides_Osemiring__div @ A )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ B @ C @ A ) @ C @ A )
= ( c_Divides_Odiv__class_Omod @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(242,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(1320,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)],[242]) ).
thf(520,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(1962,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(78,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(935,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)],[78]) ).
thf(303,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(1463,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)],[303]) ).
thf(543,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(2018,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)],[543]) ).
thf(727,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(2436,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)],[727]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ D @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) @ tc_nat ) )
| ( B = D )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(3,negated_conjecture,
~ ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ ( c_Suc @ v_ia ) ) @ ( c_Suc @ v_ja ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(755,plain,
~ ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ v_ra @ ( c_Lambda_OdB_OVar @ ( c_Suc @ v_ia ) ) @ ( c_Suc @ v_ja ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(735,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(2453,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)],[735]) ).
thf(694,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(2351,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(2106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(387,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(1653,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)],[387]) ).
thf(513,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(1944,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)],[513]) ).
thf(262,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(1367,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)],[262]) ).
thf(80,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(940,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(629,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(2206,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)],[629]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(728,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(2438,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)],[728]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( 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(2238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ A @ B ) @ C @ D )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(623,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(2191,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)],[623]) ).
thf(297,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1449,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(2495,plain,
$false,
inference(e,[status(thm)],[2163,1322,1501,1024,1369,2306,1767,1237,893,1850,941,1179,777,1295,2280,2250,1879,1337,1718,2094,1411,2336,2131,1995,2263,2480,962,1982,1750,1158,2104,1882,1068,1522,2062,994,1073,2014,1728,1205,1486,1200,2077,1924,2210,1422,2248,2114,1142,878,2380,1971,1793,1671,1655,1137,2035,1735,2448,1872,1233,814,1354,1458,1497,2195,1078,1788,1867,2184,1164,797,1275,2141,1919,2459,1342,913,1507,2360,829,2216,1001,2046,1914,2491,2020,973,1935,1650,1359,2082,2173,1529,1703,2405,1746,898,2227,1576,1228,1482,2328,2039,2269,1907,2274,1455,2488,1191,1132,949,1055,1409,1760,1298,1330,1264,1545,1892,2169,969,1568,2158,1641,1773,1362,1875,1922,817,1247,2049,1704,1890,1013,770,1398,881,1815,1494,2178,1489,1664,1811,1911,1334,1828,937,806,966,1051,905,2456,2007,1946,1465,2324,1714,1040,1109,1632,2469,2451,2236,1682,834,1858,1864,1183,1283,2073,981,1169,2281,1394,1433,2154,1696,1564,1843,2058,1896,877,1447,956,866,1886,1119,1622,2424,774,2371,2002,998,2242,988,1104,1242,849,1651,925,1306,2118,1153,761,1470,1708,1311,2232,2296,2000,1636,1047,1730,2441,1091,2428,825,1519,1580,1255,1217,1666,2032,2396,1560,1387,910,1042,952,1570,1174,1676,2133,788,1619,2150,916,1938,1968,1555,1888,1687,2200,2327,2492,1281,1291,842,1573,1106,1032,1602,2433,2477,2068,1819,1624,1836,2181,757,2345,1195,1407,1634,1392,1402,874,2100,2377,1804,1328,1064,1111,1856,980,1425,1096,869,857,1592,2300,1089,1541,1270,1259,1534,1017,1540,1006,884,1160,753,1739,2312,2080,2240,2108,1207,1644,1612,1419,1028,1082,1964,1942,901,2419,1075,1214,2349,2317,1744,1776,1150,1382,1552,1799,1984,1852,1874,1429,1720,1979,1627,1825,1324,2285,2125,1588,985,1451,2304,1266,1231,2355,1932,2465,1060,2052,2482,1599,1991,2203,1086,1779,2208,2402,1515,1026,1616,953,888,926,1712,1846,1286,1035,2368,2408,2089,773,794,2338,2121,1278,1648,965,2413,2391,1959,2253,1219,1927,1374,2260,1146,1754,2292,2028,1595,819,904,1833,1916,1884,1784,2188,1752,2016,826,1520,1226,2134,1795,1701,2161,1503,2220,1371,1733,1058,1332,1765,919,2474,1669,2193,1786,1638,1224,2148,2319,1356,764,1894,784,1524,1349,2116,1122,1690,863,1209,2119,2084,2214,2383,990,996,2246,1492,1722,1144,1376,1439,890,1877,758,1557,2111,1909,2446,848,895,1344,1293,1177,2461,811,2182,2025,1080,2314,2129,2343,1630,1993,1460,2289,943,1022,932,1952,2365,1474,1699,1245,2086,780,1113,2022,1477,851,2156,922,1973,1562,983,2075,1198,1841,1396,2212,959,2171,1066,1445,2064,1015,1364,1250,2054,1583,1809,1166,1203,1467,2271,2471,1905,2037,2234,1134,1340,1472,754,1181,836,2005,1413,1662,2096,2449,1509,2333,2256,2298,1770,887,971,1605,2175,1531,1484,1098,1547,1748,1070,872,2375,1156,2060,1400,1566,2143,2012,2407,2386,2092,2165,791,1038,1869,2276,1901,808,1679,2044,1053,1499,1790,1987,1716,1813,1300,1188,1186,1262,1235,1317,1830,1763,1658,2322,2411,1543,2113,2426,1802,1221,1427,1797,1008,2030,2266,1240,2056,1404,1898,1849,1257,2279,2357,1955,2145,1585,978,1140,1881,1272,1940,845,1839,1685,1949,1817,1913,2347,1517,1781,1126,1807,1998,2352,1084,2310,976,1010,1390,1289,1453,1590,1326,1253,813,1674,1062,1854,2431,786,781,2416,2152,2394,1646,2443,2167,2273,2283,2389,1476,896,2098,1903,2135,946,1101,1244,1822,1030,2462,2198,2066,2362,1212,1607,1513,1661,832,1442,1045,2009,1861,2399,2041,929,2330,1706,1193,2230,2294,1309,1161,1614,2421,800,1116,2287,2102,1512,2302,1725,967,835,1380,1480,2123,2218,2258,1578,1957,854,1303,1527,1148,867,1757,1436,1989,1314,2186,807,1710,2223,2340,955,1742,1693,2070,1172,767,1346,1610,2127,1352,1129,1268,860,1378,2467,822,2484,1505,2138,1093,1930,839,1384,2485,1537,2265,1019,1976,1550,908,992,1597,1431,1004,803,1320,1962,935,1463,2018,2436,1416,755,2453,2351,2106,1653,1944,1367,940,2206,1737,2438,2238,2191,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.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 16:22:13 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.62/1.05 % [INFO] Parsing done (226ms).
% 1.62/1.06 % [INFO] Running in sequential loop mode.
% 2.25/1.26 % [INFO] eprover registered as external prover.
% 2.25/1.27 % [INFO] cvc4 registered as external prover.
% 2.25/1.27 % [INFO] Scanning for conjecture ...
% 2.56/1.38 % [INFO] Found a conjecture and 752 axioms. Running axiom selection ...
% 3.07/1.50 % [INFO] Axiom selection finished. Selected 749 axioms (removed 3 axioms).
% 3.77/1.67 % [INFO] Problem is propositional (TPTP CNF).
% 3.77/1.68 % [INFO] Type checking passed.
% 3.77/1.68 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.46/3.32 % External prover 'e' found a proof!
% 10.46/3.32 % [INFO] Killing All external provers ...
% 10.46/3.32 % Time passed: 2805ms (effective reasoning time: 2251ms)
% 10.46/3.32 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.46/3.32 % Axioms used in derivation (749): cls_mult__eq__1__iff_1, cls_Suc__pred_0, cls_less__iff__diff__less__0_0, cls_min__max_Oinf__commute_0, cls_add__0__left_0, cls_add__pos__nonneg_0, cls_subst__lt_0, cls_dB_Osimps_I6_J_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, 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_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_zero__less__one_0, cls_nat__mult__eq__1__iff_1, 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_mod__mult__mult1_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_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_min__max_Oinf__sup__distrib1_0, cls_one__is__add_4, cls_Suc__n__not__n_0, cls_min__max_Ole__sup__iff_2, cls_class__semiring_Osemiring__rules_I9_J_0, cls_min__less__iff__conj_0, cls_mult__is__0_2, cls_diff__Suc__1_0, cls_dB_Osimps_I8_J_0, cls_sum__squares__eq__zero__iff_0, cls_nat__1__eq__mult__iff_0, cls_min__max_Oinf__le1_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_nat__add__left__cancel__less_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_eq__diff__iff_0, cls_min__0R_0, cls_zero__le__mult__iff_3, cls_less__antisym_0, cls_nat__mod__eq__iff_1, cls_one__le__mult__iff_0, cls_less__add__Suc2_0, cls_not__sum__squares__lt__zero_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_class__semiring_Osemiring__rules_I21_J_0, cls_mod__by__0_0, cls_add__is__1_2, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_add__le__cancel__left_1, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_min__less__iff__disj_2, cls_not__less__eq_1, cls_add__le__cancel__right_1, cls_appR_0, clsarity_nat__Orderings_Olinorder, cls_mod__add__eq_0, cls_termination__basic__simps_I1_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_nat__eq__add__iff1_0, cls_mod__add__left__eq_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_class__ringb_Onoteq__reduce_0, cls_lift__subst__lt_0, cls_add__leE_0, cls_mult__less__imp__less__right_0, cls_Suc__mult__cancel1_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_add__cancel__21_1, cls_nat__mult__1_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_mult__le__cancel__left__pos_0, cls_mod__mult__self1__is__0_0, cls_mult__nonpos__nonpos_0, cls_min__max_Oinf__sup__distrib2_0, cls_mod__mult__right__eq_0, cls_comm__monoid__add_Omult__1__right_0, cls_nat__eq__add__iff2_0, cls_sum__squares__ge__zero_0, cls_add__diff__assoc2_0, cls_add__nonpos__neg_0, cls_le__maxI2_0, cls_nat__less__add__iff1_0, cls_mod__diff__eq_0, cls_natgb_Oadd__mul__solve_0, cls_mult__less__cancel1_0, cls_nat__less__add__iff2_1, cls_le__0__eq_0, cls_mult__less__imp__less__left_0, cls_sum__squares__le__zero__iff_1, cls_dB_Osimps_I7_J_0, cls_subst__preserves__beta_0, cls_less__max__iff__disj_2, cls_eq__add__iff1_0, cls_mult__Suc__right_0, cls_add__nonneg__pos_0, cls_lem0_0, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_beta_0, cls_split__mult__neg__le_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_nat__diff__add__eq1_0, cls_gr0I_0, cls_mod__add__self2_0, cls_mult__less__cancel2_1, cls_add__gr__0_0, cls_mult__less__cancel__right__disj_3, 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_mult__mono_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__Divides_Osemiring__div, 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_add__less__mono_0, cls_n__less__n__mult__m_0, cls_nat__mult__eq__cancel1_0, cls_diff__diff__left_0, cls_mod__by__1_0, cls_class__semiring_Omul__0_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_diff__le__mono2_0, cls_Suc__le__mono_0, 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, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mod__if_1, cls_less__iff__diff__less__0_1, cls_zero__le__mult__iff_0, cls_mult__strict__mono_0, cls_subst__gt_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_mult__left__mono_0, cls_mult__strict__right__mono_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_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_mult__eq__1__iff_0, 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_mult__le__cancel1_1, cls_class__semiring_Osemiring__rules_I12_J_0, cls_Suc__leI_0, cls_add__Suc_0, cls_subst__Var_2, cls_le__imp__diff__is__add_1, cls_dB_Osimps_I3_J_0, cls_linorder__neqE__nat_0, cls_not__add__less2_0, cls_max__0R_0, 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_add__less__cancel__right_1, cls_mult__less__cancel2_2, cls_nat__add__left__commute_0, cls_trans__le__add2_0, cls_mod__mult__self1_0, cls_not__less__iff__gr__or__eq_0, cls_lift__lift_0, cls_one__is__add_5, cls_zero__le__mult__iff_4, 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_mod__add__cong_0, cls_add__left__mono_0, cls_mult__is__0_1, cls_add__nonneg__eq__0__iff_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_mod__lemma_0, cls_no__zero__divisors_0, cls_mult__le__mono_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_min__max_Ole__sup__iff_1, cls_class__semiring_Osemiring__rules_I2_J_0, cls_max__diff__distrib__left_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, cls_not__less__eq__eq_1, cls_le__iff__diff__le__0_0, cls_mult__neg__pos_0, cls_less__add__iff1_0, cls_Suc__diff__1_0, cls_min__max_Osup__left__idem_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_mod__le__divisor_0, cls_mod__Suc_0, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_add__less__mono1_0, cls_combine__common__factor_0, cls_dB_Osimps_I4_J_0, cls_min__max_Ole__infI2_0, cls_mult__pos__neg2_0, cls_nat__mult__1__right_0, cls_add__is__1_0, cls_class__ringb_Onoteq__reduce_1, cls_less__add__Suc1_0, cls_trans__le__add1_0, cls_termination__basic__simps_I4_J_0, cls_mult__right__le__imp__le_0, cls_nat__le__add__iff2_0, cls_Suc__neq__Zero_0, cls_diff__add__0_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_le__max__iff__disj_1, cls_class__semiring_Oadd__a_0, cls_min__max_Ole__iff__inf_1, cls_mod__mult__left__eq_0, cls_one__is__add_0, cls_less__Suc__eq__le_1, cls_le__mod__geq_0, cls_le__add__iff1_1, cls_min__max_Oless__supI1_0, cls_class__semiring_Osemiring__rules_I19_J_0, cls_min__max_Ole__inf__iff_0, cls_xt1_I8_J_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, cls_less__add__iff2_1, cls_mult__le__cancel__left__neg_1, cls_nat__less__add__iff2_0, cls_mult__less__cancel1_1, cls_min__max_Oinf__idem_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_termination__basic__simps_I3_J_0, cls_mult__le__cancel__left__pos_1, cls_zero__less__mult__pos_0, cls_min__max_Oinf__assoc_0, cls_mult__le__0__iff_1, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, cls_mult__le__0__iff_4, cls_min__max_Odistrib__sup__le_0, cls_min__max_Oinf__left__idem_0, cls_One__nat__def_0, cls_add__strict__mono_0, cls_mult__eq__if_1, cls_min__le__iff__disj_0, cls_le__SucE_0, cls_natgb_Onoteq__reduce_1, cls_Suc__le__mono_1, cls_linorder__linear_0, cls_nat__add__assoc_0, cls_diff__Suc__eq__diff__pred_0, cls_zero__less__two_0, cls_not__leE_0, cls_min__max_Osup__idem_0, cls_less__add__one_0, cls_class__ringb_Oadd__mul__solve_0, cls_min__max_Ole__supI_0, cls_sum__squares__eq__zero__iff_1, cls_lessI_0, cls_less__iff__Suc__add_1, cls_not__add__less1_0, clsarity_nat__Ring__and__Field_Omult__mono, cls_mult__less__cancel__right__disj_2, cls_mult__le__cancel2_2, cls_add__cancel__21_0, cls_order__trans_0, cls_eq__add__iff1_1, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_less__Suc__eq__0__disj_3, cls_diff__Suc__diff__eq1_0, cls_class__semiring_Omul__d_0, cls_natgb_Oadd__scale__eq__noteq_0, cls_nat__eq__add__iff1_1, cls_lift_Osimps_I3_J_0, cls_dB_Osimps_I1_J_0, cls_order__antisym_0, cls_le__square_0, cls_nat__1__eq__mult__iff_2, cls_mult__left__less__imp__less_0, cls_less__add__eq__less_0, cls_max__less__iff__conj_2, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_mult__le__mono1_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_mod__mult__self4_0, cls_linorder__antisym__conv1_1, cls_split__mult__pos__le_1, cls_mod__mult__cong_0, cls_no__zero__divirors__neq0_0, cls_subst__Var_1, cls_mult__Suc_0, cls_mult__le__0__iff_5, cls_diff__Suc__diff__eq2_0, cls_mult__strict__mono_H_0, cls_zero__neq__one_0, cls_le__add__iff2_1, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_diff__self_0, cls_less__imp__diff__less_0, cls_mult__le__cancel2_1, cls_diff__is__0__eq_0, cls_natgb_Oadd__cancel_0, cls_diff__less_0, cls_mod__diff__cong_0, cls_mod__Suc_1, cls_neq0__conv_1, cls_linorder__not__le_1, cls_less__1__mult_0, cls_Suc__mult__less__cancel1_1, cls_one__is__add_2, cls_min__max_Ole__sup__iff_0, cls_add__less__cancel__right_0, cls_mult__less__cancel__right__disj_5, cls_mod__mult__self2_0, cls_mult__is__0_0, cls_add__diff__cancel_0, cls_le__trans_0, cls_not__less__less__Suc__eq_0, cls_lift__preserves__beta_0, cls_add__Suc__right_0, clsarity_nat__Orderings_Opreorder, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_mult__le__mono2_0, cls_le__add__iff1_0, cls_mod__mult__distrib2_0, cls_diff__add__assoc_0, cls_nat__mult__le__cancel1_1, cls_Suc__times__mod__eq_0, cls_order__le__neq__trans_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_nat__add__right__cancel_0, cls_mult__nonneg__nonpos_0, cls_Suc__le__eq_0, cls_mult__le__cancel1_0, cls_zero__le__square_0, cls_add__diff__assoc_0, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_mod__1_0, cls_max__0L_0, cls_le__imp__diff__is__add_0, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_mult__le__cancel1_2, cls_order__eq__iff_2, cls_less__not__refl_0, cls_nat__le__add__iff1_0, cls_min__max_Oinf__greatest_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_gr0__conv__Suc_1, cls_class__ringb_Oadd__cancel_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_mod__0_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_lift__subst_0, cls_diff__less__Suc_0, cls_right__minus__eq_1, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, clsarity_nat__OrderedGroup_Oab__semigroup__mult, cls_less__add__iff1_1, cls_mult__cancel1_1, cls_linorder__neqE__ordered__idom_0, cls_mod__diff__right__eq_0, cls_add__mult__distrib_0, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_mod__add__self1_0, cls_Suc__diff__diff_0, cls_diff__cancel2_0, cls_dB_Osimps_I2_J_1, cls_class__semiring_Osemiring__rules_I3_J_0, cls_mult__eq__0__iff_2, cls_nat__1__eq__mult__iff_1, cls_sum__squares__gt__zero__iff_1, cls_mult__less__mono1_0, cls_less__diff__conv_1, cls_le__diff__conv2_0, cls_mult__less__cancel__left__neg_1, cls_nat_Oinject_0, cls_order__antisym__conv_0, cls_add__lessD1_0, cls_diff__less__mono_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_order__neq__le__trans_0, cls_subst__subst_0, cls_natgb_Onoteq__reduce_0, cls_add__nonneg__nonneg_0, clsarity_nat__Ring__and__Field_Osemiring, cls_mult__mono_H_0, cls_mod__mod__trivial_0, cls_min__max_Osup__absorb1_0, cls_le__diff__conv_0, cls_mult__strict__left__mono__comm_0, cls_class__ringb_Oadd__r0__iff_0, cls_less__diff__conv_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_add__strict__increasing_0, cls_Suc__mult__le__cancel1_1, cls_min__max_Ole__infI1_0, cls_max__less__iff__conj_1, cls_diff__mult__distrib_0, cls_nat__add__left__cancel__le_1, cls_le__add__diff__inverse_0, cls_eq__eqI_0, cls_less__eq__Suc__le_0, cls_not__less__less__Suc__eq_1, cls_Suc__mult__le__cancel1_0, cls_min__max_Oinf__sup__absorb_0, cls_linorder__less__linear_0, cls_zero__le__mult__iff_5, cls_nat__diff__add__eq2_0, cls_mult__less__mono2_0, cls_Nat_Oadd__0__right_0, cls_class__semiring_Osemiring__rules_I11_J_0, cls_nat__mult__eq__1__iff_2, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_lift_Osimps_I1_J_1, cls_Suc__lessD_0, cls_order__less__le_2, cls_nat__neq__iff_0, cls_mult__less__cancel__left__pos_1, cls_le__less__Suc__eq_0, cls_le0_0, cls_min__max_Osup__inf__distrib2_0, cls_natgb_Oadd__r0__iff_0, cls_less__eq__Suc__le_1, cls_le__eqI_0, cls_add__is__1_5, cls_nat__mult__less__cancel1_1, cls_mult__le__cancel__left__neg_0, cls_diff__self__eq__0_0, cls_le__add2_0, cls_less__Suc__eq__le_0, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_mod__less__eq__dividend_0, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_zero__le__mult__iff_1, cls_add__is__1_4, cls_min__Suc__Suc_0, cls_min__max_Ole__supI1_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_add__eq__if_1, cls_mult__le__0__iff_2, cls_nat__add__left__cancel__le_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_mult__less__cancel2_0, cls_mult__right__mono__neg_0, cls_sum__squares__eq__zero__iff_2, cls_min__max_Ole__inf__iff_2, cls_min__less__iff__conj_2, cls_nat__less__le_0, cls_lift__IT_0, cls_le__max__iff__disj_2, cls_mult__1_0, cls_zmod__simps_I2_J_0, cls_mult__less__cancel1_2, cls_mod__mult__self2__is__0_0, cls_add__mult__distrib2_0, cls_abs_0, cls_less__Suc0_0, cls_min__max_Osup__left__commute_0, cls_mod__add__right__eq_0, cls_comm__monoid__add_Omult__left__commute_0, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_le__add__right__mono_0, cls_min__max_Ole__iff__sup_1, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_nat__le__add__iff2_1, cls_diff__Suc__less_0, cls_mult__less__cancel__left__disj_3, cls_zero__less__mult__pos2_0, cls_diff__le__self_0, cls_n__less__m__mult__n_0, cls_min__max_Oinf__le2_0, cls_mod__mult__eq_0, cls_mult__less__cancel__right__disj_4, cls_mult__1__left_0, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_le__Suc__eq_2, cls_comm__monoid__add_Omult__1_0, cls_min__max_Osup__assoc_0, cls_le__cube_0, cls_min__max_Oinf__absorb2_0, cls_linorder__not__le_0, cls_nat__mult__eq__1__iff_0, cls_min__max_Oinf__left__commute_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_diff__add__assoc2_0, cls_mult__le__cancel2_0, cls_le__diff__conv2_1, cls_mod__mult__mult2_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_eq__add__iff2_0, cls_diff__less__mono2_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_mult__zero__left_0, cls_plus__nat_Oadd__0_0, cls_nat__less__le_2, cls_mod__diff__left__eq_0, cls_order__less__irrefl_0, cls_mod__mult__self3_0, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_add__nonneg__eq__0__iff_2, cls_add__is__0_2, cls_eq__eqI_1, cls_less__diff__iff_0, cls_zero__less__diff_1, cls_min__max_Oless__supI2_0, cls_add__le__mono1_0, cls_mult__left__le__imp__le_0, cls_minus__nat_Odiff__0_0, cls_add__is__1_3, cls_le__iff__add_1, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_Suc__n__not__le__n_0, cls_class__semiring_Oadd__c_0, cls_mult__pos__pos_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_Suc__leD_0, cls_add__eq__self__zero_0, cls_min__le__iff__disj_2, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_add__mono_0, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_n__not__Suc__n_0, cls_le__max__iff__disj_0, cls_min__le__iff__disj_1, cls_sum__squares__gt__zero__iff_0, cls_min__diff__distrib__left_0, cls_zmod__simps_I1_J_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_add__neg__nonpos_0, cls_mult__right__less__imp__less_0, cls_nat__less__add__iff1_1, cls_min__max_Ole__infI_0, cls_nat__le__add__iff1_1, cls_less__SucI_0, cls_nat__mult__le__cancel1_0, cls_beta__cases_I1_J_0, cls_nat__0__less__mult__iff_2, 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_subst__Abs_0, cls_min__max_Ole__iff__inf_0, cls_class__ringb_Osubr0__iff_1, cls_one__is__add_3, cls_dB_Osimps_I2_J_0, cls_mult__less__cancel__left__disj_2, cls_dB_Osimps_I5_J_0, cls_diff__add__inverse_0, cls_nat__mult__commute_0, cls_mult__less__cancel__right__disj_1, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_min__max_Ole__iff__sup_0, cls_mult__eq__self__implies__10_0, cls_less__max__iff__disj_1, cls_Suc__less__eq_0, cls_max__less__iff__conj_0, cls_order__less__imp__le_0, cls_add__leE_1, cls_Suc__pred_H_0, cls_mult__cancel1_0, cls_le__eqI_1, cls_Lambda_0, cls_Suc__diff__le_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_lift_Osimps_I1_J_0, cls_min__max_Ole__supI2_0, cls_max__add__distrib__left_0, cls_subst__Var_0, cls_add__gr__0_1, cls_min__max_Ole__supE_1, cls_diff__commute_0, cls_mod__eq__0__iff_1, cls_le__add1_0, cls_mod__if_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, cls_eq__iff__diff__eq__0_0, cls_monoid__add__class_Oadd__0__right_0, cls_mult__idem_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, clsarity_nat__Orderings_Oorder, cls_nat__mult__less__cancel1_0, cls_appL_0, cls_min__diff_0, cls_mult__le__less__imp__less_0, cls_max__Suc__Suc_0, cls_dB_Osimps_I9_J_0, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_not__one__le__zero_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_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, cls_mod__self_0, cls_less__eqI_1, cls_min__0L_0, cls_not__less__eq__eq_0, cls_sum__squares__le__zero__iff_0, cls_mod__Suc__eq__Suc__mod_0, cls_add__le__cancel__right_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_add__diff__inverse_0, cls_zero__le__mult__iff_2, cls_mod__mult__distrib_0, cls_le__refl_0, cls_min__less__iff__disj_1, cls_even__less__0__iff_0, cls_le__SucI_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0
% 10.46/3.32 % No. of inferences in proof: 1505
% 10.46/3.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2805 ms resp. 2251 ms w/o parsing
% 11.66/3.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.66/3.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------