TSTP Solution File: SWV621-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 12:17:35 EDT 2023
% Result : Unsatisfiable 18.01s 4.76s
% Output : Refutation 18.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 981
% Syntax : Number of formulae : 1877 ( 287 unt; 86 typ; 0 def)
% Number of atoms : 6031 ( 832 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 35966 (3816 ~;4240 |; 0 &;27910 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 86 usr; 7 con; 0-6 aty)
% Number of variables : 4702 ( 0 ^;4702 !; 0 ?;4702 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(v_n_type,type,
v_n: $i ).
thf(v_k_type,type,
v_k: $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oordered__ab__group__add_type,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Ring__and__Field_Ocomm__ring__1_type,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_type,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__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_Ono__zero__divisors_type,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_type,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Ozero__neq__one_type,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(class_Ring__and__Field_Omult__zero_type,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Odvd_type,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i ).
thf(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(c_HOL_Oinverse__class_Oinverse_type,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i ).
thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Oring__1_type,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(tc_bool_type,type,
tc_bool: $i ).
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_Omult__mono1_type,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_Ring__and__Field_Odivision__ring_type,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_SEQ_Obanach_type,type,
class_SEQ_Obanach: $i > $o ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(c_Transcendental_Oexp_type,type,
c_Transcendental_Oexp: $i > $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_Series_Osko__Series__Xseries__zero__1__1_type,type,
c_Series_Osko__Series__Xseries__zero__1__1: $i > $i > $i > $i ).
thf(c_Series_Osums_type,type,
c_Series_Osums: $i > $i > $i > $o ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1_type,type,
c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: $i > $i > $i > $i > $i ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(2163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(880,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(2822,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(557,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(2094,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1024,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(547,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(2072,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(1995,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(2463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(2544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(140,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(1179,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)],[140]) ).
thf(195,axiom,
! [A: $i] :
( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ tc_Complex_Ocomplex ) @ A )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(1295,plain,
! [A: $i] :
( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ tc_Complex_Ocomplex ) @ A )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(714,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(2452,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)],[714]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(664,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(2336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(564,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
thf(2109,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(574,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(2131,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(346,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(1633,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(860,axiom,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(2778,plain,
! [B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(777,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ C ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(2595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ C ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(734,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(2499,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(726,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ ( c_Suc @ C ) ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(2480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ ( c_Suc @ C ) ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(962,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
thf(1956,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).
thf(1554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Oring__char__0 @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(371,axiom,
( ( c_HOL_Oord__class_Oless @ v_n @ tc_nat )
= ( c_lessequals @ ( c_Suc @ v_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le__raw_0) ).
thf(1686,plain,
( ( c_HOL_Oord__class_Oless @ v_n @ tc_nat )
= ( c_lessequals @ ( c_Suc @ v_n ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(624,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(2250,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(562,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2104,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(2381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ B ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ B ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(994,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(623,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(2248,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)],[623]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).
thf(1728,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(1205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(893,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(2854,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(83,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1041,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(1855,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).
thf(2077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(651,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(2309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
= ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(739,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(2512,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
thf(1924,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(68,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1005,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(616,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(2231,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)],[616]) ).
thf(787,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(2622,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)],[787]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1068,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(859,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(2776,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(1808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(812,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(814,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(2676,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(2014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).
thf(1591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ tc_Complex_Ocomplex ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ B ) @ tc_Complex_Ocomplex ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
thf(2195,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) @ tc_Complex_Ocomplex ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ B ) @ tc_Complex_Ocomplex ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(1788,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(1756,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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__left_Ozero_0) ).
thf(1735,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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)],[392]) ).
thf(655,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2316,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(1327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(790,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(2627,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(41,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(945,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)],[41]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(2042,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(268,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1458,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(769,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(2575,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)],[769]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
thf(1872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(830,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(2712,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(14,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(913,plain,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(1954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(438,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
thf(1835,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(66,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1001,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odvd @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(1613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(520,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(2010,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
thf(2173,plain,
! [B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(2516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(1803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(2531,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(170,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(1243,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)],[170]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(756,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(2548,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(1650,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(1921,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(1724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(275,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( 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_mult__frac__frac_0) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( 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)],[275]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(2400,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(881,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(2825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(810,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).
thf(2667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(849,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(2755,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(828,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(2708,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(18,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(917,plain,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).
thf(2562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).
thf(2466,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(844,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).
thf(2745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(839,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(2735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
thf(1985,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Suc @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(2698,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Suc @ B ) )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(1760,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(359,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(1660,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(1907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(735,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(2501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(711,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).
thf(2444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(2185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(436,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(1832,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(33,axiom,
class_Ring__and__Field_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
thf(934,plain,
class_Ring__and__Field_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(145,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1191,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(2169,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).
thf(1890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(855,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(2767,plain,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(2158,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(526,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(2024,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(892,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(748,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(2533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(165,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1232,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(701,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(2420,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(821,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2691,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(5,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(902,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(758,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(2552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(483,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1931,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(647,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(2301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1494,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(1778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(25,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(924,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(722,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(2469,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)],[722]) ).
thf(802,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(2650,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(451,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(1858,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)],[451]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(2034,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(618,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(2237,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(251,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(1415,plain,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(785,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(2616,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__shift__lb__Suc0__0__upt_0) ).
thf(1946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).
thf(1664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(867,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).
thf(2794,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(659,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(2324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
thf(1682,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1136,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(128,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(1151,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)],[128]) ).
thf(36,axiom,
class_Ring__and__Field_Oordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
thf(937,plain,
class_Ring__and__Field_Oordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).
thf(1581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(49,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(966,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).
thf(2017,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(8,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
thf(905,plain,
class_Ring__and__Field_Oordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(981,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(442,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(482,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(1928,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
thf(1886,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(1796,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(1622,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(1351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(516,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff__right_0) ).
thf(2002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[516]) ).
thf(872,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
thf(2804,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(584,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(2154,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(504,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1975,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(853,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(884,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(2833,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)],[884]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(2281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(1896,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(727,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).
thf(2483,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(45,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(956,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(869,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).
thf(2799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
thf(2286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(846,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(2750,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(1405,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ B ) @ C @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ B ) @ C @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(773,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(2586,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(21,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(920,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(605,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).
thf(2204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(373,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(1691,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(2118,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).
thf(2047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(553,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(2083,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(97,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(1074,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)],[97]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(1604,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(800,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(2646,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(26,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
thf(925,plain,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(150,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1199,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).
thf(2364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(1915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(380,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(1708,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(413,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(1783,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(840,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(2737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(203,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(1311,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(2296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).
thf(2307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(807,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).
thf(2660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(542,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(858,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(2773,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(2000,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(90,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(1057,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)],[90]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(813,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(2673,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(774,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(2589,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(2264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(1091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(705,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(2428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(1021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(84,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1042,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(225,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1355,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).
thf(2147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(399,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1751,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(529,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ E ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
thf(2032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ E ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(746,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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_Ozero__left_0) ).
thf(2528,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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)],[746]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(470,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(1900,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(11,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(910,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(762,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(873,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(138,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(1174,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)],[138]) ).
thf(17,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(916,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(230,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(1365,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)],[230]) ).
thf(707,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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__right_Odiff_0) ).
thf(2433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[707]) ).
thf(500,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(1968,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(1951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(464,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(1888,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(660,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).
thf(2327,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ B @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ ( c_Series_Osko__Series__Xseries__zero__1__1 @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_series__zero_0) ).
thf(2345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( c_Series_Osums @ B @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ ( c_Series_Osko__Series__Xseries__zero__1__1 @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(1740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(1938,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(851,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2758,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).
thf(1837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(332,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(1602,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)],[332]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
thf(2332,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(879,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(2820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(2068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(1819,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
thf(1407,plain,
! [B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(653,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(2313,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(2492,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(842,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2741,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(347,axiom,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( 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_less__Suc0_1) ).
thf(1634,plain,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( 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)],[347]) ).
thf(240,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
thf(1392,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(615,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) @ tc_nat @ A ) @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ tc_nat ) @ tc_nat @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff__nat__ivl_0) ).
thf(2228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) @ tc_nat @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) @ tc_nat @ A ) @ A )
= ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ tc_nat ) @ tc_nat @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(2112,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(1291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(804,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(2653,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(1106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(245,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1402,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(508,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(1983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(887,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(2841,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(675,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
thf(2359,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
thf(1970,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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__right_Ozero_0) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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)],[286]) ).
thf(738,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(2509,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(792,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(2631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(796,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(2638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(632,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(2268,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)],[632]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(222,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(1350,plain,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(183,axiom,
class_SEQ_Obanach @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
thf(1270,plain,
class_SEQ_Obanach @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_1) ).
thf(1259,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(42,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(948,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)],[42]) ).
thf(870,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2801,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(301,axiom,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
thf(1534,plain,
class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(1794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(73,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
thf(1017,plain,
class_Ring__and__Field_Omult__mono1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(493,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(1953,plain,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(818,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(2685,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(304,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(1540,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)],[304]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(1006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(835,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(2724,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(385,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(1719,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)],[385]) ).
thf(895,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(2858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(750,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(2537,plain,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(718,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(2460,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(32,axiom,
class_HOL_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__HOL_Oord) ).
thf(933,plain,
class_HOL_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1461,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(4,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
thf(901,plain,
class_Ring__and__Field_Opordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(539,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1810,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(670,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(1644,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(498,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1964,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(488,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(1942,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(255,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(1424,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(652,axiom,
hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(2312,plain,
hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(723,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
thf(2472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ D @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ D @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(861,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).
thf(2781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).
thf(1419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).
thf(1668,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(733,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(2497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(765,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(2566,plain,
class_Ring__and__Field_Omult__zero @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(331,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1599,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).
thf(1979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).
thf(1825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(210,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1324,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(2504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(1776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(997,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(2125,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).
thf(1588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(106,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(1099,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)],[106]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(173,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(1249,plain,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(742,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(2519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(196,axiom,
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1297,plain,
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(816,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).
thf(2681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(885,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(2836,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(729,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(778,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(2598,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(181,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).
thf(1266,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(435,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(1831,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(146,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(1192,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(91,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1060,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ 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(1050,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)],[87]) ).
thf(771,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(2581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(720,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(2465,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
thf(911,plain,
class_Ring__and__Field_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(578,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(2140,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)],[578]) ).
thf(850,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).
thf(2756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(680,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(2370,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(22,axiom,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(921,plain,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(665,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(702,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(2423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(1732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D )
= ( c_HOL_Oinverse__class_Odivide @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(27,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
thf(926,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
thf(2634,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).
thf(1434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(450,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(1857,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(1991,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(207,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(1318,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)],[207]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(1814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(37,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(938,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(2546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(549,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(2076,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).
thf(1466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(96,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(1071,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)],[96]) ).
thf(693,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(2402,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(2408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).
thf(2089,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1515,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(2221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(808,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(2662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(9,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(906,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(837,axiom,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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_Ozero__right_0) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ 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)],[837]) ).
thf(291,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(1510,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(698,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(2413,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)],[698]) ).
thf(594,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(2176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).
thf(2391,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(2602,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Oone__class_Oone @ A ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).
thf(1631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(628,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).
thf(2260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(1146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(643,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2292,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_Transcendental_Oexp @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__minus_0) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_Transcendental_Oexp @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(2275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(582,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(2149,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)],[582]) ).
thf(832,axiom,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(2717,plain,
! [A: $i] :
( ( A
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(767,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(2570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(397,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(1747,plain,
class_Power_Opower @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(1301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
thf(1595,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(744,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).
thf(2524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2376,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
thf(1154,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(836,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(2727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).
thf(1884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(865,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(599,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).
thf(2188,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(1701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(1965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(116,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(1124,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)],[116]) ).
thf(575,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2134,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(7,axiom,
class_Ring__and__Field_Opordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
thf(904,plain,
class_Ring__and__Field_Opordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(54,axiom,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(975,plain,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).
thf(2489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(878,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(2817,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(281,axiom,
( ( c_SetInterval_Oord__class_OlessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__0_0) ).
thf(1488,plain,
( ( c_SetInterval_Oord__class_OlessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(823,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(2695,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)],[823]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(35,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(936,plain,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(528,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(2029,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(827,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(2706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(703,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(2425,plain,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).
thf(1675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(2193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(1786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( hAPP @ B @ ( c_Series_Osko__Series__Xseries__zero__1__1 @ B @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Series_Osums @ B @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_series__zero_1) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ A )
| ( ( hAPP @ B @ ( c_Series_Osko__Series__Xseries__zero__1__1 @ B @ C @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Series_Osums @ B @ ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(848,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
thf(2753,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(710,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(2442,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(852,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).
thf(2759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(716,axiom,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
thf(2457,plain,
class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(20,axiom,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(919,plain,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(768,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).
thf(2573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(226,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(1356,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)],[226]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(3,axiom,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
thf(900,plain,
class_Ring__and__Field_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(751,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(2538,plain,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(725,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).
thf(2478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(798,axiom,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ v_k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I1_J_0) ).
thf(2642,plain,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ v_k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).
thf(1894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(297,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(1524,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)],[297]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2097,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( 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_dvd__mult__cancel__right_0) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( 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)],[261]) ).
thf(501,axiom,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
thf(1969,plain,
class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(544,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(2065,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(551,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(2079,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(676,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(2361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
!= ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
= ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(788,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(2624,plain,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(1574,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(424,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).
thf(1806,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(71,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(1011,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)],[71]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(639,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(2246,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(1722,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(811,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).
thf(2669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(568,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(2116,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(886,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(2839,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(2180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
thf(2182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(2742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(781,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(2605,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(1993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(390,axiom,
class_Int_Onumber @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(1731,plain,
class_Int_Onumber @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(712,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(2446,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(697,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(2410,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)],[697]) ).
thf(16,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
thf(915,plain,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Int_Onumber @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(829,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).
thf(2710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(876,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( hAPP @ C @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) )
!= ( hAPP @ F @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) ) )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_2) ).
thf(2812,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( hAPP @ C @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) )
!= ( hAPP @ F @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) ) )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(2314,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(789,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).
thf(2625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(132,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1162,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(863,axiom,
class_Int_Onumber @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
thf(2785,plain,
class_Int_Onumber @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(776,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).
thf(2593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1556,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).
thf(2542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(943,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ C @ E @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(625,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(2252,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(809,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).
thf(2664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(636,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(2278,plain,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(661,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(2329,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(31,axiom,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(932,plain,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(770,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(1688,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(13,axiom,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(912,plain,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).
thf(2418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).
thf(1926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(376,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(1699,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)],[376]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1213,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(263,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(679,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(2369,plain,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(2535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(107,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(1102,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(737,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ tc_Complex_Ocomplex ) @ B ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__summation_0) ).
thf(2506,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ A ) @ tc_Complex_Ocomplex ) @ B ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(709,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(2439,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)],[709]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(2212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
thf(2171,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(538,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(2051,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(757,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).
thf(2550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).
thf(1245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(641,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).
thf(2288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(112,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(1113,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(868,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(2797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(2244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(847,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(2752,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(793,axiom,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
thf(2633,plain,
class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(2022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(285,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(1496,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).
thf(1694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(23,axiom,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(922,plain,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(822,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).
thf(2693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(517,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
thf(2005,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(1583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
thf(2614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ B ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).
thf(1905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(28,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(927,plain,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(2234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
| ( E
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(791,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(2629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).
thf(1958,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
!= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(2239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(1758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(2107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(2318,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).
thf(2449,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Ozero__class_Ozero @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(290,axiom,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
thf(1509,plain,
class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(38,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
thf(939,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(764,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(2564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(889,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).
thf(2846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1018,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).
thf(1770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(831,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(2715,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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__left_Odiff_0) ).
thf(1961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[497]) ).
thf(691,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(2397,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)],[691]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(2678,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(1780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(833,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(2720,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(740,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(2513,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(766,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(2567,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(398,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(1748,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)],[398]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(1798,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
thf(2298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
!= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
| ( B
= ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(579,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(2143,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(838,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(2732,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(1753,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_H_1) ).
thf(2386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 @ C @ B @ D @ A ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(891,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(2850,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(883,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(820,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(2689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ D @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(2092,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(2165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(573,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(2128,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)],[573]) ).
thf(404,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(1763,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)],[404]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(215,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(1336,plain,
class_Power_Opower @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(805,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
thf(2656,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(845,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(2747,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(1790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_1) ).
thf(2454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( c_Finite__Set_Ofinite @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(266,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(1452,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)],[266]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(179,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
thf(1262,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).
thf(1235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(101,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1085,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(1658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).
thf(2322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(825,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(2701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(1579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(393,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1738,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(159,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(1218,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(672,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(2354,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(907,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).
thf(2056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
= B )
| ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ D @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(761,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(684,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(2379,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(288,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1504,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(890,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(2848,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(2266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(1898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(445,axiom,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_k @ tc_nat ) @ v_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I2_J_0) ).
thf(1849,plain,
hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_k @ tc_nat ) @ v_n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(704,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(2426,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(507,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(1981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(637,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(2279,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(674,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).
thf(2357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(888,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).
thf(2843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( c_Suc @ D ) @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(580,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(1972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(657,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(2320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(1094,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
!= ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(834,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(2722,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(874,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( B
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(1940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(1839,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(717,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(2458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(2045,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(30,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(931,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(294,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1517,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(783,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(2611,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(806,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(2658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(866,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(2792,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(514,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).
thf(1998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(478,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(1918,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).
thf(1949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(882,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
thf(2828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(437,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(1834,plain,
class_Ring__and__Field_Omult__mono @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).
thf(1913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(903,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
thf(2347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(250,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(1412,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)],[250]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ B @ A ) @ ( c_Transcendental_Oexp @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__diff_0) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ B @ A ) @ ( c_Transcendental_Oexp @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(2110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(2305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(799,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(2643,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(688,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).
thf(2389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1,negated_conjecture,
( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex )
!= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ tc_Complex_Ocomplex ) @ v_n ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(896,plain,
( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) @ tc_nat @ tc_Complex_Ocomplex )
!= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ tc_Complex_Ocomplex ) @ v_n ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ v_k ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(642,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(344,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(527,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(2026,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)],[527]) ).
thf(448,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(1854,plain,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(782,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(2608,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(690,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
= C )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
thf(2394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
= C )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(2591,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(326,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(1590,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(634,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(894,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2855,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
= ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(350,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(1639,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)],[350]) ).
thf(576,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(2135,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)],[576]) ).
thf(695,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(2406,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Suc @ A ) @ tc_nat ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(854,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(2764,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(431,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(1822,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(745,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(2526,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(699,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).
thf(2416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(2262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(552,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(2081,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(15,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(914,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(801,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).
thf(2648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( 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_dvd__mult__cancel__left_0) ).
thf(2198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ( D
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( 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)],[603]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1513,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(2120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ tc_nat ) )
= ( hAPP @ ( c_Power_Opower__class_Opower @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(558,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
thf(2095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(524,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(2019,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)],[524]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(519,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(2009,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(2384,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(724,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(2475,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)],[724]) ).
thf(864,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(2786,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
!= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(2,axiom,
class_OrderedGroup_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
thf(899,plain,
class_OrderedGroup_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(1661,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(644,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(2294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).
thf(2036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(1309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(841,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(2739,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(732,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(2494,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
!= ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(1774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(817,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(2683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(367,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(1678,plain,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).
thf(2255,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber @ A )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(1097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ C @ A )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(164,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(1229,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)],[164]) ).
thf(743,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(2522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(2123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
= ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(627,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(2258,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ C ) @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(2374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(2102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(1395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(1625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ E ) @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
thf(1593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ E ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(877,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
thf(2815,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(518,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(2008,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(199,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(1303,plain,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_geometric__sum_0) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) @ tc_nat @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) )
| ( B
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(365,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(856,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(2768,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)],[856]) ).
thf(277,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1480,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(795,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(2636,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(429,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(1816,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)],[429]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(2334,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(826,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(2704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(678,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(2366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(2404,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(666,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(2340,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(803,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(862,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(2783,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(604,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(2201,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)],[604]) ).
thf(19,axiom,
class_Ring__and__Field_Omult__mono @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
thf(918,plain,
class_Ring__and__Field_Omult__mono @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(1363,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(214,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(1335,plain,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(2070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(613,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_0) ).
thf(2223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(786,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(2619,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
= ( c_HOL_Oone__class_Oone @ A ) )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(543,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ D ) ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Suc @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(2063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ D ) ) @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ C @ A ) @ ( c_Suc @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1742,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(620,axiom,
! [A: $i] :
( ( c_FFT__Mirabelle_Oroot @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
thf(2241,plain,
! [A: $i] :
( ( c_FFT__Mirabelle_Oroot @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(875,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_0) ).
thf(2810,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( c_Ring__and__Field_Odvd__class_Odvd @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(433,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(1827,plain,
class_Ring__and__Field_Odvd @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(505,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(1976,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)],[505]) ).
thf(772,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_1) ).
thf(2583,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ B )
| ( ( c_Finite__Set_Osetsum @ C @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B )
= ( c_Finite__Set_Osetsum @ F @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 @ D @ E @ C @ F @ A @ B ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(992,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(752,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(2539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Suc @ C ) )
= ( c_HOL_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(1299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(1902,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(2372,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ B @ tc_nat ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ A ) @ C @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff__left_0) ).
thf(2430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ A )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[706]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(871,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(2803,plain,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(779,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).
thf(2600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(728,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).
thf(2485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(303,axiom,
! [A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__zero_0) ).
thf(1537,plain,
! [A: $i] :
( ~ ( class_SEQ_Obanach @ A )
| ~ ( class_RealVector_Oreal__normed__field @ A )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
= ( c_HOL_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(819,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(2687,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).
thf(1606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(797,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(2640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).
thf(1320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ~ ( class_Int_Onumber @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(34,axiom,
class_Ring__and__Field_Odvd @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Odvd) ).
thf(935,plain,
class_Ring__and__Field_Odvd @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(708,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(2436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(2059,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
| ~ ( class_Ring__and__Field_Omult__zero @ A )
| ~ ( class_Power_Opower @ A )
| ( ( hAPP @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
thf(1944,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(940,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(923,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(2206,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ofield @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
= B )
| ( C
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(315,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(1565,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)],[315]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(1490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( B
= ( c_HOL_Ozero__class_Ozero @ A ) )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_Power_Opower__class_Opower @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(102,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(1088,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)],[102]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(1812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(1870,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ A )
| ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(857,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(2771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(2870,plain,
$false,
inference(e,[status(thm)],[2163,1322,2822,2094,1024,1168,2072,1995,1237,1031,2463,2544,1179,1295,1501,2452,1879,1337,2336,2109,2131,1633,2778,2595,1850,2499,2480,1083,962,1956,1549,1554,1110,1686,2250,1211,2104,1522,2381,1618,994,2248,1728,1205,2854,1041,1855,1200,2077,2309,2512,1924,1005,2231,2622,1068,2776,1808,2671,2676,2014,2099,1591,2114,1142,2195,1788,1671,1608,1756,1735,2316,1275,1327,2627,1988,945,2042,1507,1458,2575,1872,2712,1342,913,1063,1954,1835,2216,1001,973,1613,2010,1359,2173,2516,1803,1703,2531,1254,1243,1127,2548,1650,1921,1724,1475,2400,2825,1055,1287,1709,1792,2667,2755,2708,917,2562,2466,1132,2745,2735,1985,2698,1760,1660,1907,2501,1330,2444,2185,1577,1455,1832,934,1191,1892,2169,1890,2767,2158,2024,2852,2533,1232,1847,1545,2420,2691,902,1247,2049,2552,969,1572,1931,1568,2301,1494,1875,1778,2178,924,1911,2469,2650,1858,1828,1383,2034,2237,1415,2616,1946,1664,2794,2324,1714,1682,1136,1151,937,1581,966,1283,2073,2017,905,981,1843,1928,1377,1886,1796,1622,1351,2002,2804,2154,1975,2762,2833,2281,1896,2190,1447,2483,956,988,2799,2286,2750,1405,1696,2586,1863,920,2204,1691,1306,2118,2047,2083,1074,1604,2646,925,1199,2364,1470,1915,1708,1783,2737,1311,2296,2307,2660,1768,1868,2061,2773,2000,1047,1057,1163,2673,2589,2264,1223,1091,2428,1021,1042,1355,2147,1751,1666,2032,2528,1560,1900,910,2560,2805,1570,1174,916,1365,2433,1968,1951,1888,1656,2327,2345,1740,1938,2758,1837,1602,2332,2820,2068,1819,1195,1407,2313,2492,1281,2741,1634,1392,2228,2112,1291,2653,1106,1402,1983,2841,2359,1970,1498,2509,2631,2638,2268,1397,1350,1936,1270,1772,1259,948,2801,1534,1794,1017,1953,2685,1540,1006,1138,2724,1719,2858,2537,2460,1160,1361,933,1182,1461,901,2053,1810,2349,2038,1207,1644,1744,1964,1942,1424,2312,2472,1039,2781,1419,1668,1552,2497,2566,1429,1599,1979,1393,1825,1324,2504,1776,1263,997,2125,1588,1099,1478,1249,2519,1297,2681,1530,2836,2487,2598,1266,1831,2355,1192,1060,1050,2581,2465,984,911,1002,1852,2140,2756,1627,2370,1333,921,1563,1026,1616,2338,2423,1732,926,2634,1434,1857,1991,1318,1814,938,1241,2546,2076,1170,1466,1071,2402,2408,2089,1515,2221,953,2662,906,1278,2729,1510,2413,2176,2391,1483,1273,2602,1374,1631,2260,1146,2292,2556,1103,2275,2149,2717,1219,2570,1747,1301,1595,2524,2376,1154,2727,1884,1784,2789,2188,1652,1388,1535,1403,1701,1965,1124,2134,904,975,1620,2489,1520,2817,1226,1488,2695,1256,936,2029,1312,1865,1635,1239,2706,2425,1675,2193,1786,1271,1371,2753,2442,2759,2457,919,2573,1356,979,1209,900,2538,2478,2642,1894,1117,1524,2097,1801,1122,1439,1969,2065,2079,2361,2214,2624,1574,1806,1011,990,2284,2246,1492,1722,2669,1144,2116,2839,2180,2182,1877,2742,2605,1993,1731,2446,2410,915,1344,1177,2710,2812,1080,2314,2343,2625,1909,1162,2785,2593,1029,1149,964,1556,2542,943,2252,2664,1293,2278,2329,932,1061,2578,1688,912,2418,1926,1699,1213,1445,2086,2369,2535,1102,2156,2506,1841,2439,2212,2171,2051,2550,1245,986,2288,1113,2797,2244,2752,2633,2022,1726,1250,1496,2303,1694,922,2693,2005,1583,2614,1304,1203,1905,927,1684,2234,1134,2629,1958,1034,2239,1758,1166,2107,2318,2271,2449,1509,939,1340,2564,2846,1018,1770,2715,1961,2397,1611,1400,971,1647,2678,1368,1780,2720,1845,2513,2567,1547,1748,1798,2298,2143,2012,2732,1252,1753,2386,2850,2160,2831,2689,2092,2165,1186,2128,1763,1679,1336,2656,1711,2747,1053,1790,2454,1452,1637,1262,1235,1085,1658,2322,2701,951,1130,1579,1285,1738,1218,2354,907,2056,1934,2558,2379,1221,1427,1504,1717,2848,2266,1543,1766,1898,1849,2426,1981,1353,2279,2357,2843,2145,1485,1972,2320,1585,1094,1140,2722,1008,1881,2807,1940,1421,1839,2458,2045,931,1517,2611,1189,2658,2792,1108,1998,1918,1316,1949,2828,1157,1834,1913,976,903,2347,1654,1412,1216,2209,2110,1390,2305,1289,2226,2643,1385,2389,896,2290,2554,1481,1629,2026,1854,2608,2394,2591,1590,2167,2273,2855,1639,2135,2406,2764,1822,2526,2416,1558,2152,2262,2081,914,2648,2198,1077,1513,2120,2095,2019,1045,2009,1861,2384,2475,2786,1706,1193,899,1661,2294,2036,1309,2739,2494,1442,999,1774,2683,1678,2255,967,1097,1229,2522,2123,2218,2258,2374,1348,1642,2102,1395,1625,1593,1380,2815,2008,1303,1527,1673,2768,1480,2636,1436,1816,2334,2704,2366,1197,2404,2040,2340,2651,2783,2201,918,1363,1314,1335,2070,1172,1410,2223,960,1473,2619,1065,1346,2063,1742,928,2241,2810,1827,1976,2583,992,2539,1299,1902,1120,2372,2138,2430,1268,2803,1532,2600,2485,1537,1597,2687,1431,1606,2640,1320,935,1184,2436,2059,1416,1468,1944,940,923,2206,1463,1565,1490,1037,2351,1088,1449,1812,1014,1870,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 01:43:01 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.12 % [INFO] Parsing done (249ms).
% 1.74/1.13 % [INFO] Running in sequential loop mode.
% 2.51/1.33 % [INFO] eprover registered as external prover.
% 2.51/1.34 % [INFO] cvc4 registered as external prover.
% 2.51/1.34 % [INFO] Scanning for conjecture ...
% 2.98/1.48 % [INFO] Found a conjecture and 896 axioms. Running axiom selection ...
% 3.75/1.64 % [INFO] Axiom selection finished. Selected 894 axioms (removed 2 axioms).
% 4.51/1.87 % [INFO] Problem is propositional (TPTP CNF).
% 4.51/1.88 % [INFO] Type checking passed.
% 4.51/1.89 % [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 ...
% 18.01/4.75 % External prover 'e' found a proof!
% 18.01/4.76 % [INFO] Killing All external provers ...
% 18.01/4.76 % Time passed: 4218ms (effective reasoning time: 3621ms)
% 18.01/4.76 % 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)>
% 18.01/4.76 % Axioms used in derivation (894): cls_mult__eq__1__iff_1, cls_divide__le__eq__number__of_9, cls_less__iff__diff__less__0_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_minus__le__iff_0, cls_power__0_0, cls_le__0__eq_1, cls_divide__eq__eq_3, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_neg__0__le__iff__le_1, cls_less__divide__eq_3, clsarity_nat__HOL_Oord, cls_divide__le__eq__number__of1_9, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_k_I2_J_0, cls_root__cancel_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_atLeast0LessThan_0, cls_le__divide__eq_3, cls_order__le__less__trans_0, cls_mult__cancel2_0, cls_mult__zero__right_0, cls_zero__less__one_0, cls_divide__le__eq_2, cls_mult__nonneg__nonneg_0, cls_eq__divide__eq__number__of1_4, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_setsum__ivl__cong_1, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_zero__less__divide__iff_5, cls_divide__eq__eq__number__of_4, cls_less__divide__eq__number__of1_6, cls_le__minus__self__iff_0, cls_mult__imp__le__div__pos_0, cls_divide__pos__pos_0, clsarity_Int__Oint__Int_Onumber, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_mult_Odiff__left_0, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_mult__nonneg__nonpos2_0, cls_negative__imp__inverse__negative_0, cls_Suc__n__not__n_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_divide__le__eq__number__of_4, cls_square__eq__iff_1, cls_le__divide__eq__number__of1_0, cls_minus__zero_0, cls_mult__is__0_2, cls_Lim_Ominus__diff__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_setsum__0_0, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_exp__not__eq__zero_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_nat__lt__two__imp__zero__or__one_0, cls_inverse__eq__iff__eq_0, cls_less__antisym_0, cls_divide__less__eq__number__of1_5, cls_le__divide__eq__number__of_6, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_zero__le__divide__iff_2, cls_power__le__zero__eq_3, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, cls_divide__1_0, clsarity_Int__Oint__Orderings_Oorder, cls_power__increasing_0, cls_one__le__mult__iff_0, cls_inverse__le__1__iff_2, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, cls_divide__le__eq__number__of1_4, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, cls_divide__less__eq_4, cls_divide__le__eq_8, cls_less__divide__eq__number__of_3, cls_divide__less__eq__number__of1_0, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_divide__le__0__1__iff_1, cls_less__Suc__eq_2, cls_divide__le__eq_7, cls_not__less__eq_1, cls_minus__diff__eq_0, cls_frac__le_0, cls_compl__eq__compl__iff_0, cls_inverse__less__1__iff_2, cls_one__le__inverse__iff_2, cls_zero__less__divide__iff_0, cls_dvd__diff_0, cls_le__divide__eq__number__of1_5, cls_Suc__lessI_0, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_inverse__1_0, cls_minus__le__self__iff_0, cls_minus__divide__right_0, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_eq__divide__eq__number__of_4, cls_mult__nonpos__nonpos_0, cls_power__le__imp__le__exp_0, cls_minus__minus_0, cls_power__one_0, cls_mult__less__imp__less__right_0, cls_Suc__mult__cancel1_0, cls_left__inverse_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_neg__less__iff__less_1, cls_power__0__left__number__of_0, cls_eq__divide__eq__number__of_1, cls_left__diff__distrib__number__of_0, cls_divide__less__eq__number__of1_6, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_mult__le__cancel__left__pos_0, cls_minus__dvd__iff_1, cls_divide__eq__eq_0, cls_power__gt1_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_less__minus__iff_0, cls_power__less__imp__less__exp_0, cls_mult__less__cancel1_0, cls_split__mult__neg__le_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_mult__less__cancel__left__disj_4, cls_mult__less__imp__less__left_0, cls_le__divide__eq__number__of1_9, cls_divide__le__eq__number__of_5, cls_gr0I_0, cls_less__divide__eq_4, cls_mult__less__cancel2_1, cls_mult__less__cancel__right__disj_3, cls_inverse__divide_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_Int__Oint__Ring__and__Field_Oring__1, cls_power__less__zero__eq__number__of_1, cls_divide__strict__left__mono_0, cls_le__0__eq_0, cls_divide__le__0__iff_3, cls_mult__eq__0__iff_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_exp__diff_0, clsarity_bool__HOL_Oord, clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors, clsarity_nat__Ring__and__Field_Osemiring__0, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_nat__mult__eq__cancel1_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_divide__less__eq__number__of_6, clsarity_nat__OrderedGroup_Omonoid__mult, cls_gr__implies__not0_0, cls_mult__left__mono__neg_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict, cls_le__antisym_0, cls_less__divide__eq__number__of1_2, cls_less__eq__Suc__le__raw_0, cls_mult_Ozero__left_0, cls_setsum__shift__lb__Suc0__0__upt_0, cls_divide__neg__neg_0, cls_n__less__n__mult__m_0, cls_less__iff__diff__less__0_1, cls_nat__less__cases_0, cls_eq__divide__eq_4, cls_mult__mono_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_field__power__not__zero_0, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, cls_setsum__op__ivl__Suc_0, cls_one__le__power_0, cls_divide__eq__eq_4, cls_Suc__le__mono_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_linorder__not__less_0, cls_atLeastLessThan__empty__iff2_0, cls_inverse__le__1__iff_1, cls_power__eq__0__iff__number__of_2, cls_less__divide__eq__number__of1_0, cls_power__0__left_0, cls_order__less__asym_H_0, cls_eq__number__of_0, cls_mult_Ozero__right_0, cls_divide__le__eq__number__of_8, cls_divide__less__eq__number__of1_8, cls_class__semiring_Omul__c_0, cls_Suc__mult__less__cancel1_0, clsarity_Int__Oint__Ring__and__Field_Odvd, cls_mult__pos__neg_0, cls_nat__0__less__mult__iff_0, cls_order__eq__refl_0, cls_zero__le__mult__iff_0, cls_le__divide__eq__number__of_7, cls_divide__eq__eq__number__of1_0, cls_inverse__eq__1__iff_1, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, clsarity_Int__Oint__Ring__and__Field_Omult__mono, cls_order__le__less_0, cls_inverse__minus__eq_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, cls_linorder__antisym__conv1_0, cls_right__minus__eq_0, cls_mult__eq__1__iff_0, cls_mult__strict__right__mono_0, clsarity_fun__Orderings_Obot, cls_mult__dvd__mono_0, cls_one__le__mult__iff_2, cls_linorder__antisym__conv2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_power__le__zero__eq__number__of_0, cls_class__fieldgb_Oinverse__divide_0, cls_setsum__ivl__cong_0, cls_neg__0__le__iff__le_0, cls_minus__less__iff_1, cls_power__le__zero__eq_0, cls_mult__le__cancel1_1, cls_power__Suc2_0, cls_less__divide__eq_7, cls_le__divide__eq_7, cls_power__one__over_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_Suc__leI_0, cls_eq__divide__eq__number__of1_3, cls_dvd__mult__cancel__right_2, cls_inverse__nonpositive__iff__nonpositive_0, cls_inverse__nonnegative__iff__nonnegative_1, cls_linorder__neqE__nat_0, cls_divide__left__mono__neg_0, cls_setsum__diff__nat__ivl_0, cls_inverse__nonzero__iff__nonzero_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_less__le__not__le_2, cls_divide__neg__pos_0, cls_xt1_I10_J_0, cls_le__divide__eq_2, cls_not__less__iff__gr__or__eq_0, cls_le__divide__eq__number__of_3, cls_divide__le__eq__number__of1_6, cls_no__zero__divisors_0, cls_mult__frac__num_0, cls_neg__less__eq__nonneg_1, cls_le__imp__power__dvd_0, cls_divide__le__eq__number__of1_5, clsarity_Int__Oint__Int_Oring__char__0, cls_le__minus__iff_0, cls_mult__is__0_1, cls_less__divide__eq__number__of_7, cls_mult__less__cancel2_2, cls_neg__less__eq__nonneg_0, cls_divide__le__eq_3, cls_series__zero_1, clsarity_Complex__Ocomplex__SEQ_Obanach, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, cls_mult__le__mono_0, cls_divide__less__eq_0, cls_mult__frac__frac_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semidom, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_finite_0, cls_mult__1__right_0, cls_divide__eq__eq__number__of_3, clsarity_fun__HOL_Oord, cls_less__divide__eq_2, cls_not__less__eq__eq_1, cls_mult__neg__pos_0, clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult, cls_mult__left_Odiff_0, cls_zero__less__divide__iff_1, cls_lessThan__eq__iff_0, cls_divide__less__eq__number__of1_2, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_power__0__Suc_0, cls_divide__less__eq__number__of_0, cls_inverse__le__imp__le__neg_0, cls_mult__le__0__iff_0, cls_power__strict__increasing_0, cls_le__divide__eq__number__of1_6, cls_le__iff__diff__le__0_0, cls_mult__right__le__imp__le_0, cls_mult__pos__neg2_0, cls_divide__eq__eq__number__of1_3, cls_Suc__neq__Zero_0, clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors, cls_le__imp__inverse__le_0, cls_divide__le__eq__number__of_0, cls_power__mult_0, cls_neg__le__0__iff__le_0, cls_less__Suc__eq__le_1, clsarity_fun__Finite__Set_Ofinite_Ofinite, 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cls_Suc__less__eq_0, cls_divide__nonpos__pos_0, cls_zero__le__power_0, cls_lessThan__0_0, cls_less__divide__eq_0, cls_inverse__less__imp__less_0, cls_divide__less__eq__number__of_2, cls_mult__cancel1_0, cls_inverse__positive__imp__positive_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_power__minus_0, cls_class__semiring_Opwr__0_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_power__increasing__iff_0, cls_divide__less__eq_3, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, cls_order__less__imp__le_0, cls_le__divide__eq__number__of1_4, cls_minus__equation__iff_1, cls_atLeastLessThanSuc_1, cls_mult__idem_0, cls_less__divide__eq__number__of_5, cls_division__ring__inverse__diff_0, cls_le__divide__eq__number__of_4, cls_series__zero_0, cls_le__less__Suc__eq_1, cls_divide__less__eq__number__of1_1, cls_class__ringb_Osubr0__iff_0, cls_le__eq__less__or__eq_0, cls_dvd__mult_0, cls_le__imp__inverse__le__neg_0, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_less__Suc0_1, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_divide__le__eq__number__of1_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_zero__less__power__eq__number__of_2, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_setsum__infinite_0, cls_xt1_I7_J_0, cls_divide_Ominus_0, cls_less__divide__eq__number__of1_5, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_divide__less__0__1__iff_1, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring, cls_le__divide__eq__number__of1_8, cls_power__Suc__less_0, cls_divide__less__eq__number__of_5, cls_less__eqI_1, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_inverse__nonpositive__iff__nonpositive_1, cls_nat__mult__less__cancel1_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, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_le__neq__implies__less_0, cls_not__one__le__zero_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_0, cls_power__decreasing_0, clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_le__divide__eq__number__of_9, cls_less__divide__eq__number__of_9, cls_mult__right_Odiff_0, cls_le__divide__eq__number__of_0, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_power__mono_0, cls_divide__le__eq_1, cls_le__refl_0, cls_neg__less__iff__less_0, cls_dvd__mult__cancel__left_0, cls_dvd__power__same_0, cls_le__SucI_0, cls_divide__le__eq__number__of_3, cls_not__less__eq__eq_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_power__le__zero__eq__number__of_3, cls_power__0__left_1, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_exp__zero_0, cls_zero__le__mult__iff_2, cls_dvd__0__left_0, cls_root__summation_0, cls_divide__le__0__1__iff_0
% 18.01/4.76 % No. of inferences in proof: 1791
% 18.01/4.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4218 ms resp. 3621 ms w/o parsing
% 18.81/5.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.81/5.04 % [INFO] Killing All external provers ...
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