%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:55 AM UTC 2026
% Result : Unsatisfiable 44.16s 12.17s
% Output : Refutation 49.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1212
% Syntax : Number of formulae : 2425 ( 275 unt; 0 typ; 0 def)
% Number of atoms : 6959 (1480 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51056 (4198 ~;4534 |; 0 &;42324 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 111 usr; 9 con; 0-9 aty)
% Number of variables : 11338 ( 0 ^;11338 !; 0 ?;11338 :)
% Comments :
%------------------------------------------------------------------------------
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(t_a_decl,type,
t_a: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Oplus__class_Oplus_decl,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(v_f_decl,type,
v_f: $i ).
thf(v_m_decl,type,
v_m: $i ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__ring__1_decl,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(tc_RealDef_Oreal_decl,type,
tc_RealDef_Oreal: $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_decl,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(class_Ring__and__Field_Odivision__by__zero_decl,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(class_Ring__and__Field_Ocomm__ring_decl,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_decl,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_RealVector_Oreal__algebra_decl,type,
class_RealVector_Oreal__algebra: $i > $o ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_decl,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_Ring__and__Field_Opordered__ring_decl,type,
c_Ring__and__Field_Opordered__ring: $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(c_HOL_Oinverse__class_Odivide_decl,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i ).
thf(c_HOL_Otimes__class_Otimes_decl,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i ).
thf(c_OrderedGroup_Opordered__ab__group__add_decl,type,
c_OrderedGroup_Opordered__ab__group__add: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__meet_decl,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
thf(class_Divides_Osemiring__div_decl,type,
class_Divides_Osemiring__div: $i > $o ).
thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_RealVector_Ovector__space_decl,type,
c_RealVector_Ovector__space: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oidom_decl,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_decl,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Ring__and__Field_Oring_decl,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Ring__and__Field_Oordered__comm__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Omax_decl,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(c_Ring__and__Field_Ofield_decl,type,
c_Ring__and__Field_Ofield: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(class_RealVector_Oreal__normed__vector_decl,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_RealVector_OscaleR__class_OscaleR_decl,type,
c_RealVector_OscaleR__class_OscaleR: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__semiring__strict_decl,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(class_Ring__and__Field_Osemiring_decl,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(c_RealVector_Oadditive_decl,type,
c_RealVector_Oadditive: $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Opordered__comm__monoid__add_decl,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(c_RealVector_Obounded__bilinear_decl,type,
c_RealVector_Obounded__bilinear: $i > $i > $i > $i > $o ).
thf(c_SetInterval_Oord__class_OatMost_decl,type,
c_SetInterval_Oord__class_OatMost: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__field_decl,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Ring__and__Field_Ocomm__semiring_decl,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_Ring__and__Field_Oring_decl,type,
c_Ring__and__Field_Oring: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Omult__mono1_decl,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(c_SetInterval_Oord__class_OlessThan_decl,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(class_RealVector_Oreal__vector_decl,type,
class_RealVector_Oreal__vector: $i > $o ).
thf(class_OrderedGroup_Omonoid__add_decl,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(class_Ring__and__Field_Omult__mono_decl,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(class_Ring__and__Field_Odvd_decl,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(class_Ring__and__Field_Oordered__semidom_decl,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(class_Int_Onumber__ring_decl,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_Ring__and__Field_Oordered__semiring_decl,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Omult__zero_decl,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(class_Divides_Oring__div_decl,type,
class_Divides_Oring__div: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_RealVector_Oreal__field_decl,type,
class_RealVector_Oreal__field: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__join_decl,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_decl,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Osemigroup__add_decl,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(c_OrderedGroup_Osemigroup__add_decl,type,
c_OrderedGroup_Osemigroup__add: $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_OrderedGroup_Ocancel__ab__semigroup__add__axioms_decl,type,
c_OrderedGroup_Ocancel__ab__semigroup__add__axioms: $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1_decl,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1_decl,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__cong2__1__1_decl,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1: $i > $i > $i > $i > $i > $i ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(2630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).
thf(1767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(162,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( L @ ( K @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I29_J_0) ).
thf(1559,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( L @ ( K @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(750,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
thf(2921,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(308,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1899,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(2544,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(1001,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(3566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(2250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(2199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(792,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(3021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(173,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( F @ ( E @ ( C @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Ominus__left_0) ).
thf(1586,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( F @ ( E @ ( C @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1501,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(3944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(1411,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(621,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I32_J_1) ).
thf(2612,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1206,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oright__diff__distrib_0) ).
thf(4094,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).
thf(123,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( F @ ( H @ ( G @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__diff__eq_1) ).
thf(1469,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( F @ ( H @ ( G @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(1369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(921,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(3345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
thf(2341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(2336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(2031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1043,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I23_J_0) ).
thf(3666,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(4022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
thf(2412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(16,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
thf(1237,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1007,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatMost ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__atMost__Suc_0) ).
thf(3581,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatMost ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( C @ ( c_Suc @ hAPP ) @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(2787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(615,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
thf(2595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(1850,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(1982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(2280,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(1554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1165,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__mult) ).
thf(3990,plain,
tc_nat @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(2395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(900,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(3285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(1135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(3912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
thf(2014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(827,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(3108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1793,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(218,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
thf(1692,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(1437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(2363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(1855,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1185,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(4043,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1183,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I22_J_0) ).
thf(4037,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
thf(2309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(579,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
thf(2512,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(773,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__left__imp__eq_0) ).
thf(2976,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(403,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
thf(2117,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(758,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(2940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
thf(2104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(1199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(4075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(47,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Omult__nonpos__nonpos_0) ).
thf(1290,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1098,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(3813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(879,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(3230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(2381,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
thf(1808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(933,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(3377,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(2527,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(799,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(3040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(764,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(2953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(2590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(94,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I26_J_1) ).
thf(1401,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(963,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(3460,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(103,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I31_J_0) ).
thf(1422,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1569,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(2248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(716,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
thf(2837,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(224,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I20_J_0) ).
thf(1705,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Odiff_0) ).
thf(1788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1073,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( D @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_1) ).
thf(3745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( D @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(56,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I17_J_0) ).
thf(1310,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(749,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2918,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf_0) ).
thf(1735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(856,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1022,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(3616,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(1086,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I12_J_0) ).
thf(3781,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(332,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
thf(1954,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(2146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(118,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I39_J_0) ).
thf(1458,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1091,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(3794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(832,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(3120,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(952,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(3429,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(2035,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(929,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(3367,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
thf(4011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1036,axiom,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(3649,plain,
tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(838,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I25_J_0) ).
thf(3135,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1207,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I8_J_1) ).
thf(4097,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(2316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(918,axiom,
v_n @ ( tc_nat @ ( v_m @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less_0) ).
thf(3338,plain,
v_n @ ( tc_nat @ ( v_m @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(755,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(2933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(63,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
thf(1327,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1053,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I18_J_0) ).
thf(3693,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(2627,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(1919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(889,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(3253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(347,axiom,
! [A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(1988,plain,
! [A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1761,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1005,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
thf(3577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(2042,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(7,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1222,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
thf(3895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(897,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
thf(3276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1187,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I10_J_0) ).
thf(4047,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(2216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(978,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I5_J_0) ).
thf(3502,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(982,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I29_J_0) ).
thf(3513,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(2173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
thf(2516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(149,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(1529,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(709,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(2819,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(531,axiom,
tc_RealDef_Oreal @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).
thf(2405,plain,
tc_RealDef_Oreal @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(188,axiom,
tc_RealDef_Oreal @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oord) ).
thf(1623,plain,
tc_RealDef_Oreal @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1051,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I5_J_0) ).
thf(3688,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1029,axiom,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(3634,plain,
tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
thf(2046,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1081,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
thf(3766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(1167,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I6_J_0) ).
thf(3994,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1914,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(19,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
thf(1243,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(684,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(2763,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(1136,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I27_J_0) ).
thf(3915,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(777,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(2985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1576,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(4079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(1441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
thf(1921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1130,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(3898,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(2082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1123,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I10_J_0) ).
thf(3878,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
thf(1265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(1628,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(868,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
thf(3204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(795,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(3029,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(830,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(3116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(2755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(1004,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( B @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I4_J_0) ).
thf(3574,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( B @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(807,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).
thf(3061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(650,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
thf(2682,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(1992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(2745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(661,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(2703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).
thf(2603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(499,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
thf(2328,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(673,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
thf(2735,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(2814,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(658,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(2698,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(920,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I26_J_1) ).
thf(3342,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(2269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(2708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(1102,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( G @ ( D @ ( C @ ( F @ ( H @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( K @ ( B @ ( A @ ( J @ ( I @ ( H @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
!= ( G @ ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oeq__add__iff2_0) ).
thf(3821,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E
= ( G @ ( D @ ( C @ ( F @ ( H @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( K @ ( B @ ( A @ ( J @ ( I @ ( H @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
!= ( G @ ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(574,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(2501,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
thf(2444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(33,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
thf(1264,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(844,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(3148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1038,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
thf(3653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
thf(2274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(945,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_additive_Oadd_0) ).
thf(3410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(2185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(600,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(2562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(820,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
thf(3089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(1094,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
thf(3803,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
thf(2466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1545,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(824,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(3099,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(2713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(725,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I20_J_0) ).
thf(2857,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(596,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I23_J_1) ).
thf(2552,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(1890,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(1347,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(873,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( E @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I6_J_0) ).
thf(3216,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( E @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(909,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( E @ ( A @ ( A @ ( F @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
thf(3312,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( F @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( E @ ( A @ ( A @ ( F @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( F @ ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
thf(2158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(1059,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(3708,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(486,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
thf(2301,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(858,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(3180,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1089,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(3788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(1109,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(3840,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(932,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I12_J_0) ).
thf(3374,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(936,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__greaterThanLessThan_0) ).
thf(3385,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(964,axiom,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(3463,plain,
tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(427,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__less__0__iff__less_0) ).
thf(2169,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(1031,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(3638,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1514,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
thf(1741,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__minus__right_0) ).
thf(1398,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
thf(2635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(967,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I19_J_0) ).
thf(3470,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(779,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( C @ ( E @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_OscaleR__left_0) ).
thf(2989,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( C @ ( E @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(79,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I27_J_0) ).
thf(1362,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(1963,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1016,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( A @ ( H @ ( L @ ( K @ ( G @ ( J @ ( B @ ( I @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = H )
| ( F = H )
| ( ( F @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( G @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oadd__frac__eq_0) ).
thf(3602,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( A @ ( H @ ( L @ ( K @ ( G @ ( J @ ( B @ ( I @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = H )
| ( F = H )
| ( ( F @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( G @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(2456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(2222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(2237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(1465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
thf(2259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(636,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(2650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(2254,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(171,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I18_J_0) ).
thf(1581,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(53,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( A @ ( G @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I2_J_0) ).
thf(1302,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( A @ ( G @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1664,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(2324,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
thf(1714,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(1126,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I9_J_1) ).
thf(3887,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1156,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(3966,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(866,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(3199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(3934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(813,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
thf(3075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(1198,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= G )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I8_J_0) ).
thf(4072,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= G )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(781,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(2996,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1065,axiom,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(3724,plain,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_0) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(693,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I22_J_0) ).
thf(2782,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(2469,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( tc_nat @ ( B @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(960,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( C @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I10_J_0) ).
thf(3453,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( C @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(552,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I24_J_1) ).
thf(2451,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(968,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(3473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(1056,axiom,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(3702,plain,
tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(955,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( H @ ( G @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( I @ ( H @ ( J @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oeq__add__iff1_1) ).
thf(3438,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( H @ ( G @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( I @ ( H @ ( J @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(986,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__minus__left_0) ).
thf(3525,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(4050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(2122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1002,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__right__distrib_0) ).
thf(3569,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(2540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(905,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( B @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odiff__divide__distrib_0) ).
thf(3300,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( B @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(3923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(1960,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(2777,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(846,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(3152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(43,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
thf(1283,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
thf(2058,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(810,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
thf(3068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(1061,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I16_J_0) ).
thf(3712,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(689,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( A @ ( E @ ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(2772,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( A @ ( E @ ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(914,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Osemigroup__add ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
thf(3327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ c_OrderedGroup_Osemigroup__add ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(667,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( C @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Ozero__right_0) ).
thf(2718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( C @ c_HOL_Ozero__class_Ozero @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(2586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(938,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(3389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(768,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(2964,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(862,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(3189,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(1071,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( G @ ( K @ ( J @ ( F @ ( I @ ( C @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = G )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oadd__divide__eq__iff_0) ).
thf(3739,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( G @ ( K @ ( J @ ( F @ ( I @ ( C @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = G )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
thf(1886,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(979,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( C @ ( E @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I14_J_0) ).
thf(3505,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( C @ ( E @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1050,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( C @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__mult__cancel__left2_0) ).
thf(3685,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( C @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(1096,axiom,
( ( tc_nat @ ( v_n @ c_HOL_Oord__class_Oless ) )
= ( tc_nat @ ( v_n @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le__raw_0) ).
thf(3808,plain,
( ( tc_nat @ ( v_n @ c_HOL_Oord__class_Oless ) )
= ( tc_nat @ ( v_n @ ( c_Suc @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(584,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( A @ ( F @ ( G @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Omult__left__mono__neg_0) ).
thf(2523,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( A @ ( F @ ( G @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(2424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(774,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(2979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1047,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(3676,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(412,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I19_J_0) ).
thf(2137,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1184,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(4040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( F @ ( C @ ( A @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(927,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I8_J_0) ).
thf(3361,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(1077,axiom,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(3756,plain,
tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(1152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(3955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(885,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OatMost ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__atMost_0) ).
thf(3243,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OatMost ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(705,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I27_J_1) ).
thf(2809,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(701,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(2799,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(2286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(679,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(2750,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(221,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
thf(1697,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(998,axiom,
! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(3559,plain,
! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1018,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(3606,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
thf(2392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(2154,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1202,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I11_J_0) ).
thf(4082,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1194,axiom,
tc_nat @ class_Divides_Osemiring__div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(4065,plain,
tc_nat @ class_Divides_Osemiring__div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(954,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( C @ ( A @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__1_0) ).
thf(3435,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( C @ ( A @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(788,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(3011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
thf(2910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(217,axiom,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1691,plain,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
thf(3984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(1030,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= G )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I9_J_1) ).
thf(3635,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= G )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(861,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__scale_0) ).
thf(3186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(404,axiom,
tc_RealDef_Oreal @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
thf(2118,plain,
tc_RealDef_Oreal @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(911,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I40_J_0) ).
thf(3318,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(959,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( B @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Ominus__mult__left_0) ).
thf(3450,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( B @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(962,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(3459,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(2204,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(906,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(3303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(484,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ominus__le__iff_0) ).
thf(2296,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(804,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I19_J_1) ).
thf(3054,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1181,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I14_J_0) ).
thf(4031,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(1208,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I41_J_0) ).
thf(4100,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(2496,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(1191,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Osemigroup__add) ).
thf(4059,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(744,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(2905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1868,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(380,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( E @ ( D @ ( G @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Ole__add__iff2_1) ).
thf(2061,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( E @ ( D @ ( G @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(995,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( A @ ( A @ ( K @ ( F @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oeq__divide__imp_0) ).
thf(3550,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( A @ ( A @ ( K @ ( F @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(1048,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I24_J_0) ).
thf(3679,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(1069,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(3735,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(2705,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= B )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(1723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
thf(1355,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(27,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
thf(1255,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
thf(1217,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(1751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(1666,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1020,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(3610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_1) ).
thf(2606,plain,
! [B: $i,A: $i] :
( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(847,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(3154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
thf(4044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(547,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Osemigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__mult) ).
thf(2441,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Osemigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(892,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( H @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( H @ hAPP ) @ hAPP ) ) )
| ~ ( M @ ( L @ ( F @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofrac__eq__eq_1) ).
thf(3261,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( H @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( H @ hAPP ) @ hAPP ) ) )
| ~ ( M @ ( L @ ( F @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(8,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1223,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1060,axiom,
tc_nat @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(3711,plain,
tc_nat @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(599,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I25_J_1) ).
thf(2560,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(3972,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(1072,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( C @ ( E @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = F )
| ( D = F )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__divide__mult__cancel__left_0) ).
thf(3742,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( C @ ( E @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = F )
| ( D = F )
| ( ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(770,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(2969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(1205,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( C @ hAPP ) )
!= ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( F @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_2) ).
thf(4091,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( C @ hAPP ) )
!= ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( F @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(880,axiom,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(3233,plain,
tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(931,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G
= ( H @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I8_J_1) ).
thf(3371,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G
= ( H @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1125,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(3884,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(1099,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__lessThan_0) ).
thf(3816,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(2150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(410,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I19_J_0) ).
thf(2132,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(2414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(888,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I7_J_0) ).
thf(3250,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(869,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__imp__neg__le_0) ).
thf(3207,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(1049,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( F @ ( C @ ( H @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= G )
| ~ ( K @ ( B @ ( A @ ( J @ ( I @ ( H @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
!= ( G @ ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oeq__add__iff1_0) ).
thf(3682,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( F @ ( C @ ( H @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= G )
| ~ ( K @ ( B @ ( A @ ( J @ ( I @ ( H @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
!= ( G @ ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(919,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(3339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1085,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_0) ).
thf(3778,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(899,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( B @ ( E @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I11_J_0) ).
thf(3282,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( B @ ( E @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(732,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).
thf(2872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(2609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(1142,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(3931,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(2653,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(863,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(3191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(2464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
thf(1938,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1097,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
thf(3810,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1189,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osetsum_0) ).
thf(4053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( B @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_additive_Ozero_0) ).
thf(2433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( B @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(2477,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(1968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanLessThan__empty_0) ).
thf(2565,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(501,axiom,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
thf(2332,plain,
tc_RealDef_Oreal @ class_Int_Onumber__ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(2826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(710,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
thf(2820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(904,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
thf(3297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(977,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I18_J_0) ).
thf(3499,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(997,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I20_J_0) ).
thf(3556,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(1888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1063,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(3718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(383,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I32_J_0) ).
thf(2068,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(1819,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1624,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(990,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( G @ ( J @ ( A @ ( F @ ( I @ ( B @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = G )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( D @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__diff__eq__iff_0) ).
thf(3535,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( G @ ( J @ ( A @ ( F @ ( I @ ( B @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = G )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( D @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(1836,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(258,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
thf(1787,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(507,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( E @ ( F @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__iff__diff__less__0_1) ).
thf(2345,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( E @ ( F @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1140,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_OrderedGroup_Osemigroup__add ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
thf(3926,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_OrderedGroup_Osemigroup__add ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(2211,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(594,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( F @ ( H @ ( G @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Odiff__le__eq_1) ).
thf(2547,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( F @ ( H @ ( G @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(2313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1080,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( A @ ( A @ ( K @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__divide__eq__eq_0) ).
thf(3763,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( A @ ( A @ ( K @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(2492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(675,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ominus__less__iff_1) ).
thf(2741,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(194,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I29_J_0) ).
thf(1634,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(453,axiom,
! [A: $i] :
( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(2228,plain,
! [A: $i] :
( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(652,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I31_J_1) ).
thf(2685,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(2577,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1970,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(104,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( H @ ( A @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I1_J_1) ).
thf(1425,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( H @ ( A @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1028,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(3632,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1037,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(3650,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(4109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(1157,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( B @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I1_J_0) ).
thf(3968,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( B @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(1360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(826,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
thf(3105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(966,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( K @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__eq__divide__eq_0) ).
thf(3467,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( K @ ( D @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(1055,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(3699,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(1592,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1087,axiom,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(3784,plain,
tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1134,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I12_J_0) ).
thf(3909,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(13,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
thf(1234,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1106,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(3831,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(717,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( F @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(2840,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( F @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(971,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OlessThan ) )
= ( tc_nat @ ( A @ c_SetInterval_Oord__class_OatMost ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__Suc__atMost_0) ).
thf(3482,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OlessThan ) )
= ( tc_nat @ ( A @ c_SetInterval_Oord__class_OatMost ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(946,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( D @ ( C @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( D @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__inverse__eq__divide_0) ).
thf(3413,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( D @ ( C @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = E )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( D @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(30,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1259,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(761,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
thf(2946,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= B )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(520,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( E @ ( G @ ( D @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oless__add__iff1_1) ).
thf(2377,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( E @ ( G @ ( D @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(702,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(2801,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(1804,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1117,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(3862,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(2509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(825,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
thf(3102,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1155,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I27_J_0) ).
thf(3963,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(298,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Odiff__left_0) ).
thf(1878,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(937,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(3386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(670,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
thf(2726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(669,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(2724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(230,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(1719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(2537,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(882,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( D @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oinverse__eq__divide_0) ).
thf(3237,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( B @ ( D @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1147,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I25_J_1) ).
thf(3941,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(819,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( D @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oless__add__iff1_0) ).
thf(3087,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( D @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(791,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(3018,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(134,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I31_J_0) ).
thf(1493,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(363,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I33_J_0) ).
thf(2023,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(841,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
thf(3143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(783,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
thf(3000,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(944,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= F )
| ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(3407,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= F )
| ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(538,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I34_J_0) ).
thf(2419,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(956,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(3441,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(1584,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
thf(2666,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= B )
| ( ( A @ c_HOL_Ozero__class_Ozero )
!= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = F )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( E @ ( F @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__right__imp__eq_0) ).
thf(1644,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = F )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( E @ ( F @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I1_J_0) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(3294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(1084,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( K @ ( F @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__eq__imp_0) ).
thf(3775,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( K @ ( F @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(840,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(3141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1151,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( C @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I13_J_0) ).
thf(3952,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( C @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(2877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(1292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1024,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(3622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(822,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(3094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(119,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I24_J_0) ).
thf(1461,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(730,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I3_J_1) ).
thf(2868,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( C @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1014,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( H @ ( K @ ( A @ ( G @ ( J @ ( B @ ( I @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = H )
| ( F = H )
| ( ( F @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( G @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odiff__frac__eq_0) ).
thf(3596,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( H @ ( K @ ( A @ ( G @ ( J @ ( B @ ( I @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = H )
| ( F = H )
| ( ( F @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( G @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( G @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(459,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = F )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( E @ ( F @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__cancel__right_0) ).
thf(2240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = F )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( E @ ( F @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(283,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( A @ ( H @ ( G @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I4_J_0) ).
thf(1842,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( A @ ( H @ ( G @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1700,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(796,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(3032,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(269,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ominus__less__iff_0) ).
thf(1810,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(2,negated_conjecture,
( ( t_a @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( v_f @ c_Finite__Set_Osetsum ) ) ) @ ( v_m @ ( v_f @ hAPP ) @ ( t_a @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( t_a @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( v_f @ c_Finite__Set_Osetsum ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1214,plain,
( ( t_a @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( v_f @ c_Finite__Set_Osetsum ) ) ) @ ( v_m @ ( v_f @ hAPP ) @ ( t_a @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( t_a @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( v_f @ c_Finite__Set_Osetsum ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(864,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Odiff__right_0) ).
thf(3194,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ hAPP ) )
= ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_additive_Ominus_0) ).
thf(2349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ hAPP ) )
= ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
thf(2108,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(369,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I25_J_1) ).
thf(2038,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(113,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(1446,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1039,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I21_J_0) ).
thf(3656,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(2581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(329,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( B @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__diff__eq_0) ).
thf(1947,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( B @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1026,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
thf(3628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(916,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I6_J_0) ).
thf(3333,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(1979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(413,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(2140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(147,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I26_J_0) ).
thf(1525,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(1057,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(3703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(276,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( F @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Ominus__right_0) ).
thf(1825,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( F @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(62,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__right__diff__distrib_0) ).
thf(1324,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1249,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(582,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(2519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(834,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(3126,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(992,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( B @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(3541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( B @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(488,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(2304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(87,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I21_J_0) ).
thf(1382,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(567,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(2487,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(720,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).
thf(2845,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(806,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
thf(3059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(924,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(3354,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1196,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( C @ ( E @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = F )
| ( B = F )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__divide__mult__cancel__right_0) ).
thf(4068,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( C @ ( E @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = F )
| ( B = F )
| ( ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(2387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(341,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I37_J_0) ).
thf(1974,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(460,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I22_J_0) ).
thf(2243,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(1932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(875,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__atLeastLessThan_0) ).
thf(3222,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
thf(2006,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(264,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I25_J_0) ).
thf(1799,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(1145,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I7_J_0) ).
thf(3937,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(1079,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(3760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(1429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(887,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G
= ( H @ ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I9_J_0) ).
thf(3247,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G
= ( H @ ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(727,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
thf(2862,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(686,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(2766,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(376,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(2052,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(565,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I36_J_0) ).
thf(2482,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(2272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(928,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( D @ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = D )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__self_0) ).
thf(3364,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( D @ ( H @ ( G @ ( F @ ( C @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( B = D )
| ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(817,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
thf(3083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(851,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(3162,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(867,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
thf(3201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(91,axiom,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(1393,plain,
! [A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(843,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
thf(3147,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(752,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
thf(2926,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
thf(1779,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(1695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(3173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(1115,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I23_J_0) ).
thf(3856,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(2402,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(2529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(235,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I18_J_1) ).
thf(1732,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(969,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( B @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I9_J_0) ).
thf(3476,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( B @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1103,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3824,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(290,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( A @ ( E @ ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(1857,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( A @ ( E @ ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1107,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I5_J_0) ).
thf(3834,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(660,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
thf(2702,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1000,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ hAPP ) @ hAPP ) )
= E )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oright__inverse__eq_1) ).
thf(3563,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ hAPP ) @ hAPP ) )
= E )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(898,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(3279,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(1010,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I15_J_0) ).
thf(3587,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(860,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I33_J_0) ).
thf(3183,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(378,axiom,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(2057,plain,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(1012,axiom,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(3592,plain,
tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(1846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(907,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
thf(3306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(2076,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(678,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
thf(2748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(1169,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( B @ ( H @ ( G @ ( F @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I4_J_0) ).
thf(3999,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( B @ ( H @ ( G @ ( F @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(912,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I15_J_0) ).
thf(3321,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1032,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(3639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(748,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__minus__left_0) ).
thf(2915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( B @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(2408,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(698,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( F @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(2793,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( F @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( F @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring )
| ~ ( A @ class_Ring__and__Field_Odvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(980,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I16_J_0) ).
thf(3508,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(1895,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(949,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(3422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( tc_nat @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__add__nat__ivl_0) ).
thf(3841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( tc_nat @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(1171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(4004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(504,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I24_J_0) ).
thf(2338,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(2235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(2729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(482,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( C @ ( B @ ( E @ ( D @ hAPP ) @ c_RealVector_Oadditive ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Oadditive__right_0) ).
thf(2292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( C @ ( B @ ( E @ ( D @ hAPP ) @ c_RealVector_Oadditive ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1127,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Oadd__right_0) ).
thf(3890,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(129,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( C @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__0__less__iff__less_0) ).
thf(1483,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( C @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(38,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
thf(1273,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(828,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I35_J_0) ).
thf(3111,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1176,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I36_J_0) ).
thf(4017,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1054,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
thf(3696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(849,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(3158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1041,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( C @ ( H @ ( G @ ( F @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I3_J_0) ).
thf(3660,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( C @ ( H @ ( G @ ( F @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
thf(2001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(24,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1251,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(836,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(3130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(926,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( H @ ( G @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( J @ ( H @ ( I @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oeq__add__iff2_1) ).
thf(3358,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( H @ ( G @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( J @ ( H @ ( I @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Oring ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(1120,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(3871,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( c_Suc @ hAPP ) )
!= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(367,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__0__le__iff__le_1) ).
thf(2033,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(800,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(3042,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( D = E )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(610,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(2585,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1019,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(3607,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(3079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(2570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(365,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I28_J_0) ).
thf(2028,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(176,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__0__less__iff__less_1) ).
thf(1595,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(1884,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(2525,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(95,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( E @ ( D @ ( G @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oless__add__iff2_1) ).
thf(1403,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( A @ ( K @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( E @ ( D @ ( G @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(766,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).
thf(2959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(994,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I39_J_0) ).
thf(3547,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(881,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I18_J_0) ).
thf(3234,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(2048,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(757,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I22_J_1) ).
thf(2938,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
thf(1615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(1784,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(697,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__less__iff__less_1) ).
thf(2791,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(883,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(3240,plain,
tc_nat @ class_Ring__and__Field_Oordered__semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(696,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(984,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( B @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Otimes__divide__eq__left_0) ).
thf(3519,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( B @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(435,axiom,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(2188,plain,
! [A: $i] :
( ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_additive_Odiff_0) ).
thf(1620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( E @ ( C @ hAPP ) @ ( D @ ( C @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(568,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(2489,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(201,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I23_J_0) ).
thf(1652,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(1070,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I8_J_0) ).
thf(3736,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(816,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).
thf(3081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
thf(2016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(602,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__le__iff__le_0) ).
thf(2568,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1535,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(704,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__left__commute_0) ).
thf(2806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(1011,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(3590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(943,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(3404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1119,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(3868,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(708,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(2817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
thf(1226,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(656,axiom,
tc_RealDef_Oreal @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).
thf(2695,plain,
tc_RealDef_Oreal @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(28,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1256,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(2134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1015,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(3599,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(876,axiom,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(3223,plain,
tc_nat @ class_Ring__and__Field_Opordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(257,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
thf(1786,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(2326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(756,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
thf(2935,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(1997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
thf(2442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(973,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I14_J_0) ).
thf(3487,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(1023,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I17_J_0) ).
thf(3619,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(947,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Ominus__mult__minus_0) ).
thf(3416,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(29,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1258,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(854,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I30_J_0) ).
thf(3170,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(1675,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(989,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(3532,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(3118,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1075,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(3751,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(449,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(2220,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(225,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I33_J_0) ).
thf(1707,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(803,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(3051,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
thf(2891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(1066,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(3726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(36,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1271,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(814,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(3077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1035,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I15_J_0) ).
thf(3646,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(1212,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(4112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).
thf(915,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(3330,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_nat @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(674,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(2738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(1042,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( G @ ( J @ ( A @ ( F @ ( I @ ( C @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = G )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odiff__divide__eq__iff_0) ).
thf(3663,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( G @ ( J @ ( A @ ( F @ ( I @ ( C @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = G )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
thf(1865,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(66,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
thf(1332,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(3123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(307,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( E @ ( D @ ( A @ ( K @ ( J @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oless__add__iff2_0) ).
thf(1897,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( E @ ( D @ ( A @ ( K @ ( J @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(598,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I38_J_0) ).
thf(2557,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(821,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(3091,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(2474,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(925,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(3355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(2148,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(512,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I31_J_0) ).
thf(2358,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(583,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(2521,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(648,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(2679,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(633,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(948,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( E @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I5_J_0) ).
thf(3419,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( E @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(461,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( E @ ( D @ ( K @ ( A @ ( J @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Ole__add__iff2_0) ).
thf(2246,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( E @ ( D @ ( K @ ( A @ ( J @ ( C @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( H @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(155,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( D @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Ozero__left_0) ).
thf(1542,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( E @ ( B @ c_HOL_Ozero__class_Ozero @ ( D @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(644,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(2669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(839,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(2079,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
thf(2361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2311,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(668,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).
thf(2721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
thf(2119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1027,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(3631,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
thf(1853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(2084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(2214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(626,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(2624,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(305,axiom,
tc_RealDef_Oreal @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).
thf(1894,plain,
tc_RealDef_Oreal @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(778,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
thf(2987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(631,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Odiff__right_0) ).
thf(2637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(2422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(1806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1153,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I34_J_0) ).
thf(3957,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(690,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
thf(2774,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(895,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osetsum_0) ).
thf(3270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(1589,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1068,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( B @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__minus__divide__divide_0) ).
thf(3732,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( B @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(2284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(865,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
thf(3197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(265,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( L @ ( K @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I30_J_1) ).
thf(1801,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( L @ ( L @ ( K @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= K )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(859,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Osemigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) ).
thf(3182,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Osemigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1009,axiom,
tc_nat @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(3586,plain,
tc_nat @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(809,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Osplit__mult__pos__le_1) ).
thf(3066,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(741,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__cancel__right_1) ).
thf(2896,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero @ ( E @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(1376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(2197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(850,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I19_J_1) ).
thf(3160,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A
= ( B @ ( c_Suc @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(874,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__mult__cancel__left_0) ).
thf(3219,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( C = F )
| ( ( E @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(433,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I32_J_0) ).
thf(2182,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(629,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(2632,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(69,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(1339,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(506,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( A @ ( H @ ( G @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I3_J_0) ).
thf(2343,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( A @ ( H @ ( G @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(812,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(3073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(2757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(733,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I26_J_0) ).
thf(2874,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1158,axiom,
tc_nat @ class_Ring__and__Field_Omult__zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(3971,plain,
tc_nat @ class_Ring__and__Field_Omult__zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
thf(2278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(753,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
thf(2928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(1128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(3893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(961,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(3456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(2180,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(837,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( F @ ( H @ ( G @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__diff__eq_1) ).
thf(3133,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( F @ ( H @ ( G @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1209,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(4103,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
!= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).
thf(1193,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(4064,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(2267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1180,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__left__distrib_0) ).
thf(4028,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( D @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ c_RealVector_Oadditive ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Oadditive__right_0) ).
thf(1821,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ c_RealVector_Oadditive ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1093,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( A @ ( I @ ( H @ ( G @ ( B @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__minus__divide__right_0) ).
thf(3800,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( A @ ( I @ ( H @ ( G @ ( B @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(1003,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(3572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(1909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(852,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(3165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(292,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( D @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__left__diff__distrib_0) ).
thf(1862,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( F @ ( E @ ( D @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) )
= ( F @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( F @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(534,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( E @ ( G @ ( D @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Ole__add__iff1_1) ).
thf(2410,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( I @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( H @ ( F @ ( E @ ( G @ ( D @ ( I @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( H @ ( E @ ( G @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(281,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I21_J_1) ).
thf(1838,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(614,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(2593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(785,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
thf(3006,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( D @ ( B @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__zero__left_0) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( D @ ( B @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(2542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(464,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( C @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Odiff__le__eq_0) ).
thf(2252,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( A @ ( C @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(642,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Osplit__mult__pos__le_0) ).
thf(2664,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( C @ ( G @ ( A @ ( B @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
thf(2461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(772,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(2974,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(718,axiom,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(2842,plain,
tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
thf(1952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(845,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(3150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(500,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(2329,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
thf(2770,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(1396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(2171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1,negated_conjecture,
t_a @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(1213,plain,
t_a @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(2086,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(1477,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__cancel__left_1) ).
thf(2101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(135,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I32_J_0) ).
thf(1496,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(857,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I20_J_1) ).
thf(3178,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
thf(2207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(655,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(2693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(767,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I28_J_1) ).
thf(2962,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(515,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
thf(2365,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(685,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
thf(2765,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1203,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( E @ ( H @ ( G @ ( A @ ( D @ ( F @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = E )
| ( ( C @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__inverse_0) ).
thf(4085,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( E @ ( H @ ( G @ ( A @ ( D @ ( F @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = E )
| ( ( C @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_OscaleR_0) ).
thf(2369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(754,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
thf(2931,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(2288,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(884,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(3241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(700,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(2797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(790,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I27_J_0) ).
thf(3016,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(2752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(922,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( D = F )
| ( ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__mult__cancel__right2_0) ).
thf(3348,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( D = F )
| ( ( E @ ( D @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
thf(2156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(576,axiom,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
thf(2506,plain,
tc_RealDef_Oreal @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(974,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I14_J_0) ).
thf(3490,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(934,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I38_J_0) ).
thf(3380,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(163,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I23_J_0) ).
thf(1562,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(377,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
thf(2054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(763,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(2952,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(1304,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(2471,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= B )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(1160,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( I @ ( H @ ( B @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__cancel__right_0) ).
thf(3975,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( I @ ( H @ ( B @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = E )
| ( ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(742,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I16_J_0) ).
thf(2899,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(355,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Odvd,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
thf(2005,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Odvd,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1124,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ominus__divide__left_0) ).
thf(3881,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(190,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__minus__iff_1) ).
thf(1626,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(985,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( E @ ( C @ ( D @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1 ) ) ) ) @ ( B @ hAPP ) )
!= ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1 ) ) ) ) @ ( D @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__cong_1) ).
thf(3522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( E @ ( C @ ( D @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1 ) ) ) ) @ ( B @ hAPP ) )
!= ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong__1__1 ) ) ) ) @ ( D @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(787,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( E @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__iff__diff__less__0_0) ).
thf(3009,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( E @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(957,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I40_J_0) ).
thf(3444,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(458,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
thf(2239,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2318,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(940,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(3395,plain,
! [A: $i] :
( A
!= ( A @ ( c_Suc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(1045,axiom,
tc_nat @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(3672,plain,
tc_nat @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(311,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( D @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__less__0__iff__less_1) ).
thf(1905,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( D @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1162,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__ivl__cong_1) ).
thf(3981,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( B @ ( A @ ( F @ ( C @ ( E @ ( D @ c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 ) ) ) ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( C @ c_Finite__Set_Osetsum ) ) ) )
= ( B @ ( A @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( F @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Ocomm__monoid__add )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(2503,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(40,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I36_J_0) ).
thf(1277,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(407,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I30_J_0) ).
thf(2124,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(551,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
thf(2449,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_RealVector_Oadditive ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadditive__right_0) ).
thf(1509,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ c_RealVector_Oadditive ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
thf(1990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(802,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(3048,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(3921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(70,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__minus__iff_1) ).
thf(1340,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(502,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(2256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I9_J_0) ).
thf(2597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(334,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__less__iff__less_0) ).
thf(1958,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(759,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( H @ ( A @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I2_J_1) ).
thf(2942,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( H @ ( A @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(580,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__cancel__left_0) ).
thf(2513,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( F @ ( D @ ( C @ hAPP ) @ hAPP ) ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__zero__right_0) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(485,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I35_J_0) ).
thf(2298,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(1770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(666,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(2715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(528,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( D @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Ole__add__iff1_0) ).
thf(2397,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( D @ ( C @ ( K @ ( A @ ( J @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( I @ ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(2661,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(2375,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(437,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( F @ ( H @ ( G @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Odiff__less__eq_1) ).
thf(2192,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( F @ ( H @ ( G @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(872,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(3214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(199,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I20_J_0) ).
thf(1647,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(1040,axiom,
! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(3659,plain,
! [A: $i] : ( A @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(1150,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( H @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I8_J_0) ).
thf(3949,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( H @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(647,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
thf(2678,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(430,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I26_J_0) ).
thf(2175,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(870,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(3209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(150,axiom,
tc_RealDef_Oreal @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
thf(1531,plain,
tc_RealDef_Oreal @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(738,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(2888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(736,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( L @ ( L @ ( K @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I29_J_1) ).
thf(2882,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( L @ ( L @ ( K @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(714,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(910,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(3315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(2143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1132,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__zero__left_0) ).
thf(3904,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(2588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(1076,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Oab__semigroup__add) ).
thf(3754,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(672,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(2732,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(25,axiom,
tc_bool @ class_Lattices_Oboolean__algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(1252,plain,
tc_bool @ class_Lattices_Oboolean__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(2850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(2160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1033,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I13_J_0) ).
thf(3642,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(808,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(3063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
thf(2700,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(1177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(4020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(474,axiom,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(2276,plain,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(1579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1062,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( B @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oadd__divide__distrib_0) ).
thf(3715,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( B @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(2656,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(1499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1146,axiom,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(3940,plain,
tc_nat @ class_Ring__and__Field_Oordered__semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(451,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(2224,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( E @ ( A @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(554,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I21_J_0) ).
thf(2454,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__eq__0__iff_2) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ c_HOL_Ozero__class_Ozero @ ( D @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(2165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1101,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I6_J_0) ).
thf(3818,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( E @ ( G @ ( F @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( E @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1052,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(3691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(195,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__minus__iff_0) ).
thf(1637,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(829,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(3114,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(2688,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(896,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(3273,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1090,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( B @ ( F @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( C @ hAPP ) )
= ( A @ ( F @ ( E @ ( F @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_additive_Osetsum_0) ).
thf(3791,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_RealVector_Oadditive ) ) )
| ( ( B @ ( F @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( C @ hAPP ) )
= ( A @ ( F @ ( E @ ( F @ ( A @ ( B @ ( D @ ( C @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
thf(3026,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(542,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I26_J_1) ).
thf(2429,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1235,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(1901,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(993,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I7_J_0) ).
thf(3544,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( E @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(1105,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I28_J_0) ).
thf(3828,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(496,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( E @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__iff__diff__le__0_0) ).
thf(2322,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( E @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1112,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oleft__diff__distrib_0) ).
thf(3847,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
thf(1738,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(4,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
thf(1218,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1114,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( H @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I7_J_1) ).
thf(3853,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J
= ( K @ ( K @ ( J @ ( H @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) ) )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1082,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( C @ ( E @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I12_J_0) ).
thf(3769,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( J @ ( C @ ( E @ ( I @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(646,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(2675,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(780,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(2992,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(975,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( C @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I3_J_0) ).
thf(3493,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( C @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(607,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
thf(2579,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(1504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(1717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(811,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(3071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(721,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(2848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(786,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
thf(3007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(941,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( H @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I8_J_1) ).
thf(3398,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( H @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(901,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I9_J_0) ).
thf(3288,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(1702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(6,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
thf(1221,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OscaleR_0) ).
thf(1955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(2843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(340,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( C @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Odiff__less__eq_0) ).
thf(1972,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( C @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( B @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(2711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(1210,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(4106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Osemiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).
thf(139,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I34_J_0) ).
thf(1506,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(877,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I9_J_0) ).
thf(3224,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( F @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(793,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(3024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(726,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(2860,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
thf(2949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= C )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(83,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I28_J_0) ).
thf(1372,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(890,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(3256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C = E )
| ( ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(299,axiom,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
thf(1881,plain,
! [A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(37,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1272,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(848,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(3156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(1240,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(2760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(2924,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(1149,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I7_J_1) ).
thf(3946,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1008,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(556,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(2458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(372,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
thf(2045,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(1966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(737,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(2885,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( B
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ( ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(657,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(2696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1817,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(60,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__meet,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).
thf(1321,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__meet,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(958,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(3447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(438,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I37_J_0) ).
thf(2194,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1141,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
thf(3928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(384,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(2071,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( F @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(853,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(3168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).
thf(2352,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1078,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(3757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(2479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(942,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I24_J_0) ).
thf(3401,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(2088,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( C @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(1949,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(731,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I25_J_0) ).
thf(2870,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(713,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(1121,axiom,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(3874,plain,
tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
thf(2347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(1781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(1025,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( B @ ( E @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I13_J_0) ).
thf(3625,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( B @ ( E @ ( I @ ( H @ ( G @ ( F @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1200,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(4078,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(676,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(2490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(2110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero )
= ( A @ ( B @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1192,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( D @ ( F @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__inverse_0) ).
thf(4061,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( D @ ( F @ ( A @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) @ ( B @ ( D @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
thf(2907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(1092,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I17_J_0) ).
thf(3797,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(1013,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( I @ ( H @ ( B @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = E )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__cancel__left_0) ).
thf(3593,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( E @ ( I @ ( H @ ( B @ ( G @ ( A @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = E )
| ( ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(1067,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).
thf(3729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_nat @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__eq__0__iff_1) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ ( A @ ( C @ c_RealVector_Ovector__space ) ) )
| ~ ( B @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(588,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(2532,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(935,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(3383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(917,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Omonoid__add) ).
thf(3336,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__add )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(711,axiom,
! [A: $i] :
( ( ( A @ c_Lattices_Oupper__semilattice__class_Osup )
= ( A @ c_Orderings_Oord__class_Omax ) )
| ~ ( A @ class_Lattices_Oupper__semilattice )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__max_0) ).
thf(2823,plain,
! [A: $i] :
( ( ( A @ c_Lattices_Oupper__semilattice__class_Osup )
= ( A @ c_Orderings_Oord__class_Omax ) )
| ~ ( A @ class_Lattices_Oupper__semilattice )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(240,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
thf(1745,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(771,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
thf(2971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).
thf(2431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(930,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I15_J_0) ).
thf(3368,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(818,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(3085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1021,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( C @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__lessThan__Suc_0) ).
thf(3613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( C @ ( B @ hAPP ) @ ( A @ ( tc_nat @ ( tc_nat @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(477,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
thf(2283,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(2389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(2098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(972,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__shift__bounds__Suc__ivl_0) ).
thf(3484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( c_Suc @ hAPP ) @ ( C @ ( c_Suc @ hAPP ) @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( c_Suc @ ( B @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(724,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(2855,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(2853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(2290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(1104,axiom,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( I @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( I @ hAPP ) @ hAPP ) ) )
| ~ ( M @ ( L @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = F )
| ( E = F )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofrac__eq__eq_0) ).
thf(3825,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ ( I @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( I @ hAPP ) @ hAPP ) ) )
| ~ ( M @ ( L @ ( F @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = F )
| ( E = F )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(310,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(1903,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).
thf(2406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(2811,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
thf(3991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(1074,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( H @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Oprod__diff__prod_0) ).
thf(3748,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( H @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( F @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( H @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( G @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( G @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( H @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( C @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(2026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(784,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(3003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(20,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
thf(1244,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1173,axiom,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(4010,plain,
tc_nat @ class_OrderedGroup_Oab__semigroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(983,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(3516,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(146,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I4_J_1) ).
thf(1523,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( B @ ( I @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(409,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( D @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__le__0__iff__le_1) ).
thf(2130,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( D @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(1116,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(3859,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(2152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(2262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(2009,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(523,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(2384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
!= ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(913,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I25_J_0) ).
thf(3324,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( I @ ( H @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= H )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
thf(2066,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(988,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(3529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(424,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I29_J_0) ).
thf(2162,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(649,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
thf(2680,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(181,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
thf(1607,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(923,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(3351,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(743,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(2902,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(2095,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(571,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I22_J_0) ).
thf(2494,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( C @ ( A @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_0) ).
thf(1994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(2447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(760,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(2944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(765,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(2956,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(1491,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1161,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( G @ ( K @ ( J @ ( F @ ( I @ ( B @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = G )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( D @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Odivide__add__eq__iff_0) ).
thf(3978,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( G @ ( K @ ( J @ ( F @ ( I @ ( B @ ( H @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( D = G )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( E @ ( D @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(747,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ ( F @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(2912,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( A @ ( F @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(2399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(1111,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I11_J_0) ).
thf(3844,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(635,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__0__le__iff__le_0) ).
thf(2648,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( D @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1777,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(894,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_nat @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff__nat__ivl_0) ).
thf(3267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_nat @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_nat @ ( E @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( tc_nat @ ( tc_nat @ ( E @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ ( tc_nat @ ( tc_nat @ ( D @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(2230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( D
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
thf(2294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1034,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(3645,plain,
tc_nat @ class_Ring__and__Field_Omult__mono1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1179,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I35_J_0) ).
thf(4025,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(692,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(2779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1642,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1175,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( D = F )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ononzero__mult__divide__mult__cancel__right_0) ).
thf(4014,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( F @ ( J @ ( I @ ( B @ ( H @ ( A @ ( G @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( E = F )
| ( D = F )
| ( ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(2534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) )
= C )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(1164,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( E @ ( C @ ( D @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1 ) ) ) ) @ ( B @ hAPP ) )
!= ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1 ) ) ) ) @ ( D @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__cong2_1) ).
thf(3987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ ( E @ ( C @ ( D @ c_Finite__Set_Osetsum ) ) ) ) )
| ( ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1 ) ) ) ) @ ( B @ hAPP ) )
!= ( A @ ( E @ ( D @ ( B @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xsetsum__cong2__1__1 ) ) ) ) @ ( D @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(893,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( H @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I7_J_0) ).
thf(3264,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( K @ ( J @ ( E @ hAPP ) @ hAPP ) @ ( H @ hAPP ) @ hAPP ) )
= J )
| ~ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(976,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I10_J_1) ).
thf(3496,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( J @ ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ ( F @ hAPP ) @ hAPP ) )
= I )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(2003,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(414,axiom,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
thf(2142,plain,
tc_RealDef_Oreal @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(651,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(2683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1058,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( C @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I2_J_0) ).
thf(3705,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( C @ ( A @ ( H @ ( G @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(41,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
thf(1280,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(1678,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1088,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(3785,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= E )
| ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
!= ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(981,axiom,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_OrderedGroup_Ocancel__ab__semigroup__add__axioms ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cancel__ab__semigroup__add__class_Oaxioms_0) ).
thf(3511,plain,
! [A: $i] :
( ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_OrderedGroup_Ocancel__ab__semigroup__add__axioms ) )
| ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(902,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( E @ ( C @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_Oadd__left_0) ).
thf(3291,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( F @ ( E @ ( C @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( D @ hAPP ) @ hAPP ) @ ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(1168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(3997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(1133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(3907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(776,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(2983,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1118,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I28_J_0) ).
thf(3865,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(3837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(965,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(3464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( D @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(148,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( B @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oless__diff__eq_0) ).
thf(1527,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( A @ ( I @ ( B @ ( H @ ( G @ ( F @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(1673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(22,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
thf(1248,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(375,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(2050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(687,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( A @ ( G @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I1_J_0) ).
thf(2768,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( F @ ( I @ ( H @ ( A @ ( G @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(128,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I19_J_0) ).
thf(1480,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I
= ( J @ ( J @ ( I @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(1859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(441,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(2201,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(1122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(3875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1172,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(4007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(3850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Int_Onumber__ring )
| ~ ( A @ class_Ring__and__Field_Oidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(516,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(2366,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(2091,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(951,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I13_J_0) ).
thf(3426,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( A @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(1182,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(4034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( E @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Oring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(3045,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(1095,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(3805,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(2549,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( B
= ( A @ ( C @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(908,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( B @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Ominus__mult__right_0) ).
thf(3309,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( B @ ( G @ ( F @ ( A @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) @ ( C @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(842,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(3145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(999,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I42_J_0) ).
thf(3560,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(604,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
thf(2572,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( E @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( E @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(970,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( C @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Otimes__divide__eq__right_0) ).
thf(3479,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( L @ ( K @ ( J @ ( I @ ( H @ ( A @ ( G @ ( C @ ( F @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(98,axiom,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
thf(1410,plain,
tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(537,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( A @ ( F @ ( G @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Omult__right__mono__neg_0) ).
thf(2417,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( B @ ( H @ ( A @ ( F @ ( G @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ~ ( C @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1288,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(699,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(2795,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(624,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ominus__le__iff_1) ).
thf(2619,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(950,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(3424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1046,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
thf(3673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(2021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(381,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(2063,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(886,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I11_J_0) ).
thf(3244,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1352,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( ( A @ ( c_Suc @ hAPP ) )
= B )
| ( B @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(469,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( E @ ( F @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__iff__diff__le__0_1) ).
thf(2265,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( E @ ( F @ ( D @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( E @ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(2507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(939,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(3392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(1197,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(4071,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(518,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(2372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(15,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1236,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(408,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(2127,plain,
! [B: $i,A: $i] :
( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(835,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(3128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(1977,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(769,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(2966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( C @ ( A @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_Divides_Osemiring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
thf(1268,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(805,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Oneg__le__0__iff__le_0) ).
thf(3057,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( G @ ( A @ ( F @ ( B @ ( D @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ ( D @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(2803,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
| ( B
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(1532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(2600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(1017,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
thf(3605,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(2485,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1083,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(3772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(1550,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(2583,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_nat @ ( A @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ ( c_Suc @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(891,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(3259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1195,axiom,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(4066,plain,
! [A: $i] :
~ ( A @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(1100,axiom,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(3817,plain,
tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(1923,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(991,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Oring__simps_I26_J_0) ).
thf(3538,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H
= ( I @ ( I @ ( H @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(1925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(728,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(2864,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(1137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_1) ).
thf(3918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(1204,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( F @ ( J @ ( I @ ( E @ ( H @ ( G @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = F )
| ( D = F )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oinverse__add_0) ).
thf(4088,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( A @ ( F @ ( J @ ( I @ ( E @ ( H @ ( G @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( C = F )
| ( D = F )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).
thf(987,axiom,
tc_nat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(3528,plain,
tc_nat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1006,axiom,
tc_nat @ class_Ring__and__Field_Omult__mono,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(3580,plain,
tc_nat @ class_Ring__and__Field_Omult__mono,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(823,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( A @ ( F @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( F @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__bilinear_OscaleR__right_0) ).
thf(3096,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( D @ c_RealVector_Obounded__bilinear ) ) ) )
| ( ( G @ ( A @ ( F @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) @ ( E @ ( D @ hAPP ) @ hAPP ) )
= ( G @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( F @ c_RealVector_OscaleR__class_OscaleR ) @ hAPP ) ) )
| ~ ( C @ class_RealVector_Oreal__normed__vector )
| ~ ( B @ class_RealVector_Oreal__normed__vector )
| ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(2436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
thf(1848,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(953,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).
thf(3432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(715,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
thf(2834,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( A @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(1064,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I17_J_0) ).
thf(3721,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( E @ ( D @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(797,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(3035,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(1131,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ring_Oring__simps_I16_J_0) ).
thf(3901,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( B @ c_Ring__and__Field_Opordered__ring ) ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(789,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(3013,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(3960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) )
= ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
thf(2672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(735,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(2879,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) )
= ( A @ ( C @ ( D @ ( F @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
| ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
!= ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
| ~ ( A @ class_Divides_Oring__div ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(632,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
thf(2640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(495,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
thf(2321,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(878,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I10_J_0) ).
thf(3227,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(1367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(871,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(3212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(2690,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( B @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(782,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
thf(2998,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(361,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vector__space_Oscale__eq__0__iff_0) ).
thf(2018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( B @ c_HOL_Ozero__class_Ozero ) )
| ( E
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ ( B @ ( C @ c_RealVector_Ovector__space ) ) )
| ( ( E @ ( D @ ( C @ hAPP ) @ hAPP ) )
!= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( B @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(729,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
thf(2866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ ( A @ ( C @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(546,axiom,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( L @ ( L @ ( K @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Ofield__eq__simps_I30_J_0) ).
thf(2438,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K
= ( L @ ( L @ ( K @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
| ~ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(132,axiom,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1490,plain,
! [A: $i] : ( A @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(622,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(2615,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( C @ ( A @ ( D @ c_HOL_Otimes__class_Otimes ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(553,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(2453,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1190,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = A )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field_Oright__inverse__eq_0) ).
thf(4056,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = A )
| ~ ( J @ ( I @ ( B @ ( H @ ( G @ ( F @ ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Ring__and__Field_Ofield ) ) ) ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1449,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(270,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ole__minus__iff_0) ).
thf(1812,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( H @ ( A @ ( G @ ( F @ ( C @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ~ ( B @ ( C @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1143,axiom,
tc_nat @ class_OrderedGroup_Omonoid__add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(3933,plain,
tc_nat @ class_OrderedGroup_Omonoid__add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(996,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(3553,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(431,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pordered__ab__group__add_Ogroup__simps_I21_J_0) ).
thf(2177,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( K @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ c_OrderedGroup_Opordered__ab__group__add ) ) ) ) ) ) )
| ( ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(638,axiom,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__join,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) ).
thf(2655,plain,
tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__join,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(1170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(4002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_lessequals ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_lessequals ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ( A @ ( tc_nat @ ( B @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL )
| ( B @ ( c_Suc @ hAPP ) @ ( tc_nat @ ( A @ c_HOL_Oord__class_Oless ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1044,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ring_Ominus__mult__commute_0) ).
thf(3669,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( A @ ( G @ ( F @ ( B @ ( E @ c_Ring__and__Field_Oring ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(4177,plain,
$false,
inference(e,[status(thm)],[2630,1767,1559,2921,1899,2544,3566,2250,2199,3021,1322,1586,1501,3944,1411,2612,4094,1469,1369,1823,3345,2341,2336,2031,3666,4022,1729,2412,1237,1840,3581,2787,2595,1850,2499,2427,1982,2280,1554,3990,2395,3285,3912,2014,3108,1793,1692,1437,2363,1855,4043,4037,2309,2512,2976,2117,2940,2104,4075,1290,3813,3230,2381,1443,1808,2659,3377,2527,3040,2953,2590,1401,3460,1422,1569,2248,2114,2837,1705,1788,3745,1310,2918,1735,3175,1872,3616,3781,1954,2146,1458,3794,1608,3120,3429,2035,3367,4011,3649,3135,4097,1999,2316,3338,2933,1327,3693,2627,1260,1919,3253,1988,1761,1342,3577,2042,1222,3895,3276,2575,4047,1746,2216,3502,3513,1935,1475,2173,2516,1529,2819,2405,1623,3688,3634,2046,3766,3994,1914,1243,2763,3915,2985,1576,4079,1441,1650,1921,3898,2082,3878,1518,1265,1628,3204,3029,3116,2755,3574,3061,2682,1313,1992,2745,2703,2603,2328,2735,2814,2698,1298,3342,2269,2708,3821,1907,2501,1330,2444,1264,3148,3653,1511,2274,3410,2185,2562,3089,3803,2466,1545,3099,2713,2857,2552,1890,1347,3216,3312,2158,3708,2301,3180,1232,3788,3840,1892,3374,3385,3463,1379,2169,3638,1514,1741,1398,2635,3470,2989,1362,1963,3602,1875,2456,2222,2237,1465,2259,2650,1828,2254,1581,1302,1664,2324,1714,3887,3966,3199,3934,3075,4072,2996,3724,1911,2782,2893,1632,2469,3453,2451,3473,3702,3438,3525,4050,2122,3569,2540,3300,3923,1960,2777,3152,1283,2073,2058,3068,2190,3712,2772,3327,2718,2586,3389,2964,3189,3739,1886,3505,3685,3808,2523,2424,2979,3676,2137,4040,3361,3756,3955,3243,2809,1345,2799,2286,2750,1405,1697,3559,3606,2392,2154,1521,4082,4065,3435,3011,2910,1691,3984,3635,3186,2118,3318,2093,3450,3459,2204,3303,2296,2307,3054,4031,4100,2496,2621,4059,2905,1868,2061,3550,3037,3679,3735,2705,1723,1355,1255,1217,1751,1666,1487,3610,2606,3154,4044,1274,2441,3261,1223,3711,2560,3972,3742,2969,4091,3233,3371,3884,3816,2150,2132,2414,3250,3207,3682,3339,3778,1238,3282,1602,2872,1687,2609,2112,3931,2653,3191,2464,1938,1365,3810,4053,2433,2477,1968,2565,2332,2826,2820,3297,3499,3556,1888,1296,3718,2068,1819,1624,3535,1836,1787,2345,3926,2211,1407,2547,2313,3763,2492,1281,2741,1634,2228,2685,1328,2577,1970,1425,3632,3650,4109,3968,1360,3105,3467,3699,1592,3784,3909,1234,3831,2840,3482,3413,1772,1259,2946,2377,2801,1804,3862,2509,3102,1540,3963,1878,3386,2726,2724,1719,2537,3237,1755,3941,3087,3018,1567,1493,2023,3143,3000,3407,2419,3441,1584,2666,1644,1612,3294,1419,3775,3141,3952,2877,1942,1659,1292,3622,3094,1461,2868,3596,1414,2240,1842,1700,3032,1810,1791,1214,3194,2349,2108,2038,1446,3656,2581,1947,1984,3628,3333,1979,2140,1525,3703,1825,1324,1249,2519,3126,3541,1451,2304,1456,1382,2487,2845,3059,3354,4068,2387,1668,1974,1552,2243,2355,1932,3222,2006,1799,3937,3760,1429,3247,2862,2766,2052,2482,1599,2272,3364,3083,3162,3201,1393,3147,2926,1814,1779,1695,3173,3856,2402,2529,1732,3476,1333,3824,1857,3834,1318,2702,3563,3279,3587,3183,2057,3592,1846,1712,3306,2076,2748,3999,1286,3321,3639,2915,2408,2793,3508,1895,2645,3422,3841,2617,4004,2338,2235,2729,2292,3890,1483,1273,3111,4017,3696,1374,3158,3660,2001,1251,1764,3130,3358,3871,2033,3042,2585,1219,3607,3079,2570,1548,1927,2028,1595,1884,2525,1388,1403,2959,3547,1833,3234,2048,2938,1615,1784,2791,3240,2789,3519,2188,2981,1620,2489,1652,3736,3081,2016,2568,1535,2806,1795,3590,3404,3868,2817,1226,2695,1256,2134,3599,3223,1786,2326,2935,1997,2442,3487,3619,3416,1258,3170,1675,3532,3118,3751,2220,1707,3051,2891,3726,1271,3077,3646,4112,3330,2738,3663,1865,1332,3123,1897,2557,3091,2474,3355,1224,2148,2358,2521,2679,2642,3419,2246,1542,2669,3138,2079,2361,2311,2721,2119,3631,1853,2084,2214,2624,1894,2987,2637,2422,1574,1806,3957,2774,1349,3270,1589,3732,2284,3197,1801,3182,3586,3066,2896,1571,1376,1439,2197,3160,1307,3219,2182,1471,2632,1339,2343,3073,2757,2874,3971,2278,2928,3893,3456,2180,3133,4103,4064,1630,2267,4028,1821,3800,3572,1909,3165,1862,2410,1838,2785,2593,3006,1556,2542,2252,2664,2461,2974,2842,1952,3150,2329,2770,1396,2171,1213,2086,1477,2101,1726,1496,3178,2207,2693,2962,2365,2765,1245,4085,2369,2931,2288,3241,2797,3016,1775,2752,1435,3348,2156,2506,3490,3380,1562,2054,2952,1304,1758,1467,2471,3975,2899,2005,3881,1626,3522,3009,3444,2239,2318,3395,3672,1905,3981,2503,1684,1277,2124,2449,1509,1990,3048,3921,1340,2333,2256,2597,1958,2942,2513,1748,2298,1770,2715,2397,2661,2375,1743,2192,3214,1647,3659,3949,2678,2175,3209,1753,1531,2888,2882,2831,1516,3315,2143,2012,3904,1605,2588,3754,2732,1252,2850,2160,3642,3063,2700,4020,2276,1830,1579,3715,2656,1499,3940,2224,2454,1432,2165,3818,1300,3691,1637,3114,2688,3273,3791,3026,2429,1262,1235,1901,3544,3828,2322,1538,3847,1738,1218,3853,1336,3769,2675,2992,3493,2579,1504,1717,3071,2848,3007,3398,3288,1702,2379,1221,1284,1955,2843,1485,1972,2711,4106,1506,3224,1427,1670,1797,3024,2860,2949,1372,3256,1881,1272,3156,1240,1617,2760,2924,3946,3584,2458,2045,1966,2885,2696,1817,1321,3447,2194,3928,2071,3168,1940,1316,2352,3757,2479,3401,2088,1949,2870,2828,1844,3874,2347,1654,1781,2209,3625,4078,2743,2490,2110,1390,2226,1453,4061,2907,3797,3593,3729,2167,2554,2532,3383,3336,2823,1745,2971,2431,3368,3085,3613,1253,1385,1721,2283,2389,2098,3484,2855,1639,2853,2290,3825,1903,2406,2811,3991,3748,2026,3003,1244,4010,3516,1523,2130,3859,2152,2262,2009,2384,3324,2066,3529,2162,2680,1607,3351,1661,2902,2095,2494,1994,2447,2944,2956,1491,1689,3978,2912,2399,3844,2648,1777,3267,1294,2230,2294,3645,4025,2779,2218,1642,4014,2534,3987,3264,1986,3496,2003,2142,2302,2683,3705,1280,1678,3785,3511,3291,3997,3907,2983,3865,1229,2233,3837,3464,1527,1673,1248,2050,2768,1480,1859,2201,3875,4007,3850,2366,2091,3426,4034,2040,3045,3805,2549,3309,3145,1657,3560,1693,2572,3479,1410,2417,1288,1710,2795,1473,2619,3424,3673,2021,2063,1610,1930,3244,1352,2265,2507,3392,4071,2372,1236,2127,3128,1977,2966,1268,3057,2803,1532,2600,3605,2485,3772,1550,1357,2583,3259,4066,3817,1923,3538,1925,1597,2864,3918,4088,3528,3580,3096,1681,2436,1848,1416,3432,2834,3721,3035,3901,3013,3960,2672,2879,2640,2321,3227,1367,1945,3212,2690,1463,2998,1565,2018,2866,2438,1490,2615,1917,2453,4056,1449,1812,2106,3933,3553,2177,2655,4002,1870,3669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/0.42 % Computer : n018.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 14:34:51 UTC 2026
% 0.18/0.42 % CPUTime :
% 0.18/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.30/1.17 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.83/1.94 % [INFO] Parsing done (760ms).
% 3.83/1.96 % [INFO] Running in sequential loop mode.
% 4.86/2.55 % [INFO] eprover registered as external prover.
% 4.86/2.56 % [INFO] Scanning for conjecture ...
% 6.12/2.93 % [INFO] Found a conjecture (or negated_conjecture) and 1223 axioms. Running axiom selection ...
% 7.98/3.34 % [INFO] Axiom selection finished. Selected 1210 axioms (removed 13 axioms).
% 10.02/3.85 % [INFO] Problem is propositional (TPTP CNF).
% 10.02/3.90 % [INFO] Type checking passed.
% 10.47/3.90 % [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 ...
% 44.26/12.14 % External prover 'e' found a proof!
% 44.26/12.14 % [INFO] Killing All external provers ...
% 44.26/12.14 % Time passed: 11574ms (effective reasoning time: 10171ms)
% 44.16/12.17 % Axioms used in derivation (1210): cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, clsarity_fun__Lattices_Olower__semilattice, cls_vector__space_Oscale__zero__right_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_add__0__left_0, cls_le__divide__eq_8, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_minus__le__iff_0, cls_ring_Oring__simps_I21_J_0, cls_ring_Oring__simps_I20_J_1, cls_order__le__less__trans_0, cls_less__divide__eq_3, cls_inf__sup__aci_I2_J_0, cls_semigroup__add__class_Oaxioms_0, cls_ring_Oring__simps_I22_J_1, cls_field_Ofield__eq__simps_I26_J_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_field_Ononzero__divide__mult__cancel__right_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_neg__0__le__iff__le_1, cls_finite__atMost_0, clsrel_OrderedGroup_Ocomm__monoid__add_OrderedGroup_Osemigroup__add, cls_le__divide__eq_3, cls_pordered__ring_Oring__simps_I11_J_0, cls_field_Ononzero__divide__mult__cancel__left_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_sup__max_0, cls_mult__zero__right_0, cls_ring_Oeq__add__iff1_1, cls_sup__ge1_0, cls_divide__le__eq_2, cls_order__eq__iff_0, cls_finite__atLeastLessThan_0, cls_pordered__ring_Oring__simps_I7_J_0, cls_zero__less__divide__iff_5, cls_ring_Ominus__mult__commute_0, cls_mod__mult__mult1_0, cls_field_Ofield__eq__simps_I30_J_1, cls_divide__pos__pos_0, cls_pordered__ring_Oring__simps_I23_J_0, cls_field_Ofield__eq__simps_I9_J_0, cls_mult__imp__le__div__pos_0, cls_pordered__ring_Oring__simps_I27_J_1, cls_pordered__ring_Oring__simps_I28_J_1, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_pordered__ab__group__add_Oneg__0__le__iff__le_0, cls_compl__sup_0, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_dvd__mult__right_0, cls_pordered__ring_Oring__simps_I17_J_0, cls_field_Ofield__eq__simps_I21_J_0, cls_Suc__inject_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_DERIV__mult__lemma_0, cls_order__less__le__trans_0, cls_divide__less__0__iff_0, clsarity_RealDef__Oreal__RealVector_Oreal__field, cls_comm__semiring__class_Odistrib_0, cls_setsum__ivl__cong_1, cls_pordered__ring_Omult__nonpos__nonpos_0, cls_pordered__ring_Oring__simps_I37_J_0, cls_Suc__mono_0, cls_divide_OscaleR_0, cls_le__minus__self__iff_0, cls_lessThan__Suc__atMost_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_scaleR__cancel__right_1, cls_setsum__head__upt__Suc_0, cls_Suc__n__not__n_0, cls_left__minus_0, cls_min__max_Ole__sup__iff_2, cls_mult_Oadditive__right_0, cls_square__eq__iff_1, clsarity_nat__Lattices_Odistrib__lattice, cls_termination__basic__simps_I5_J_0, cls_Lim_Ominus__diff__minus_0, cls_mult_Odiff__left_0, cls_field_Odivide__zero__left_0, cls_pordered__ring_Oring__simps_I32_J_1, cls_xt1_I12_J_0, cls_additive_Oadd_0, cls_pordered__ab__group__add_Ole__minus__iff_1, cls_field_Ofield__eq__simps_I37_J_0, cls_sum__squares__eq__zero__iff_0, cls_divide__nonpos__neg_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_minus__zero_0, cls_scaleR_Oadd__right_0, cls_mult__less__cancel__left__disj_1, clsarity_RealDef__Oreal__RealVector_Oreal__vector, cls_pordered__ab__group__add_Oless__minus__iff_0, cls_pordered__ring_Oring__simps_I9_J_0, cls_field_Ofield__eq__simps_I8_J_1, cls_distrib__sup__le_0, cls_inf__sup__aci_I6_J_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_zero__le__divide__iff_2, cls_class__semiring_Osemiring__rules_I21_J_0, cls_add__increasing2_0, cls_bounded__bilinear_Oprod__diff__prod_0, cls_pordered__ring_Oring__simps_I8_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, clsarity_bool__Lattices_Olower__semilattice, cls_mod__by__0_0, cls_mod__mod__cancel_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, 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cls_pordered__ab__group__add_Ogroup__simps_I29_J_0, cls_divide__le__eq_1, cls_pordered__ring_Oring__simps_I16_J_0, clsarity_RealDef__Oreal__RealVector_Oreal__algebra
% 44.16/12.17 % No. of inferences in proof: 2425
% 44.16/12.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11574 ms resp. 10171 ms w/o parsing
% 49.18/13.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.18/13.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------