TSTP Solution File: SWW216+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:22:06 EDT 2023
% Result : Theorem 21.43s 5.94s
% Output : Refutation 22.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1310
% Syntax : Number of formulae : 2514 ( 726 unt; 108 typ; 0 def)
% Number of atoms : 6776 (1724 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 33753 ( 445 ~; 138 |; 660 &;28938 @)
% ( 278 <=>;3294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 108 usr; 13 con; 0-4 aty)
% Number of variables : 4963 ( 0 ^;4951 !; 12 ?;4963 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i > $i ).
thf(v_da_____type,type,
v_da____: $i ).
thf(v_m_____type,type,
v_m____: $i ).
thf(v_e_type,type,
v_e: $i ).
thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
thf(tc_Code__Numeral_Ocode__numeral_type,type,
tc_Code__Numeral_Ocode__numeral: $i ).
thf(c_Int_Osucc_type,type,
c_Int_Osucc: $i > $i ).
thf(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
thf(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
thf(c_Int_Opred_type,type,
c_Int_Opred: $i > $i ).
thf(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
thf(c_Int_OPls_type,type,
c_Int_OPls: $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Rings_Ocomm__semiring_type,type,
class_Rings_Ocomm__semiring: $i > $o ).
thf(class_Rings_Oordered__semiring_type,type,
class_Rings_Oordered__semiring: $i > $o ).
thf(class_Groups_Oab__semigroup__add_type,type,
class_Groups_Oab__semigroup__add: $i > $o ).
thf(class_Groups_Ouminus_type,type,
class_Groups_Ouminus: $i > $o ).
thf(class_Groups_Oone_type,type,
class_Groups_Oone: $i > $o ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Groups_Ocomm__monoid__mult_type,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
thf(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(class_Rings_Ono__zero__divisors_type,type,
class_Rings_Ono__zero__divisors: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_Groups_Oab__semigroup__mult_type,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
thf(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
thf(class_Groups_Omonoid__add_type,type,
class_Groups_Omonoid__add: $i > $o ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).
thf(class_Rings_Oordered__cancel__semiring_type,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
thf(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
thf(class_Rings_Osemiring__0_type,type,
class_Rings_Osemiring__0: $i > $o ).
thf(class_Rings_Osemiring_type,type,
class_Rings_Osemiring: $i > $o ).
thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Rings_Oordered__comm__semiring_type,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
thf(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
thf(class_Groups_Ocancel__semigroup__add_type,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Groups_Oordered__comm__monoid__add_type,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(c_Int_Oiszero_type,type,
c_Int_Oiszero: $i > $i > $o ).
thf(class_Rings_Omult__zero_type,type,
class_Rings_Omult__zero: $i > $o ).
thf(class_Groups_Oordered__ab__semigroup__add_type,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
thf(class_Int_Oring__char__0_type,type,
class_Int_Oring__char__0: $i > $o ).
thf(class_Rings_Olinordered__semiring_type,type,
class_Rings_Olinordered__semiring: $i > $o ).
thf(class_Groups_Olinordered__ab__group__add_type,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
thf(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
thf(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).
thf(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i ).
thf(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
thf(class_Rings_Oring__1_type,type,
class_Rings_Oring__1: $i > $o ).
thf(class_Rings_Odivision__ring_type,type,
class_Rings_Odivision__ring: $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Fields_Olinordered__field__inverse__zero_type,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
thf(class_Groups_Osgn__if_type,type,
class_Groups_Osgn__if: $i > $o ).
thf(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: $i > $i > $i ).
thf(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: $i > $i > $i ).
thf(class_RealVector_Oreal__normed__field_type,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(class_Rings_Odivision__ring__inverse__zero_type,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
thf(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
thf(class_Rings_Olinordered__semiring__1__strict_type,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
thf(class_Rings_Olinordered__semiring__1_type,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
thf(class_Rings_Oring__1__no__zero__divisors_type,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
thf(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
thf(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(c_Transcendental_Oexp_type,type,
c_Transcendental_Oexp: $i > $i ).
thf(class_SEQ_Obanach_type,type,
class_SEQ_Obanach: $i > $o ).
thf(c_Deriv_Oderiv_type,type,
c_Deriv_Oderiv: $i > $i > $i > $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
thf(c_Transcendental_Oln_type,type,
c_Transcendental_Oln: $i ).
thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
thf(class_Rings_Oordered__ring__abs_type,type,
class_Rings_Oordered__ring__abs: $i > $o ).
thf(class_Rings_Oordered__ring_type,type,
class_Rings_Oordered__ring: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra__1_type,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(class_Groups_Oabs__if_type,type,
class_Groups_Oabs__if: $i > $o ).
thf(class_Rings_Oring__no__zero__divisors_type,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(class_Rings_Olinordered__ring__strict_type,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
thf(c_Transcendental_Oarctan_type,type,
c_Transcendental_Oarctan: $i ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(class_Lattices_Oab__semigroup__idem__mult_type,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
thf(v_d_____type,type,
v_d____: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(class_RealVector_Oreal__normed__div__algebra_type,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).
thf(2163,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).
thf(1665,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(141,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(1586,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1161,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__inj__iff) ).
thf(4909,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(160,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
thf(1633,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(682,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
thf(3399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(811,axiom,
class_Groups_Oabs__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
thf(3798,plain,
class_Groups_Oabs__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1104,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ! [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ E @ D )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ C @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__pos__inc__right) ).
thf(4729,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ! [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ E @ D )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ C @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(695,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
thf(3434,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(681,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
thf(3397,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(698,axiom,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
thf(3449,plain,
class_Rings_Olinordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(346,axiom,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
thf(2331,plain,
class_Rings_Osemiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(735,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
thf(3566,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(1153,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(4877,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
thf(4447,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(863,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
thf(3962,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(187,axiom,
! [A: $i] :
( ( c_Int_Osucc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
thf(1718,plain,
! [A: $i] :
( ( c_Int_Osucc @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
thf(2612,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(908,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
thf(4094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1137,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
thf(4835,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(221,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
thf(1823,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1018,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
thf(4450,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(882,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln) ).
thf(4005,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(580,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
thf(3053,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(911,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ! [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ E @ D )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ C @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ E ) ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__neg__dec__right) ).
thf(4101,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ? [D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
& ! [E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ E @ D )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ C @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ E ) ) @ ( hAPP @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(933,axiom,
! [A: $i] :
( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
thf(4183,plain,
! [A: $i] :
( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(869,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
thf(3979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__comm__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(826,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__gt__zero) ).
thf(3830,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power2) ).
thf(2480,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( c_Power_Opower__class_Opower @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
thf(1982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( c_Power_Opower__class_Opower @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1159,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
thf(4904,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(615,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
thf(3172,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(622,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ~ ( c_Int_Oiszero @ A @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).
thf(3185,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ~ ( c_Int_Oiszero @ A @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(875,axiom,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
thf(3990,plain,
class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__even__eq) ).
thf(2512,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(247,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).
thf(1924,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__vector @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1035,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
thf(4500,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(722,axiom,
class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
thf(3509,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(596,axiom,
class_Groups_Oone @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
thf(3098,plain,
class_Groups_Oone @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(1178,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
thf(4960,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(1269,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1182,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(4973,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(51,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
thf(1305,plain,
class_Groups_Ocancel__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
thf(1437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Power_Opower__class_Opower @ D @ B @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).
thf(2077,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(731,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
thf(3534,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(1168,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_Transcendental_Oln @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__mult) ).
thf(4931,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_Transcendental_Oln @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).
thf(547,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
thf(2940,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Osgn__if @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).
thf(1596,plain,
! [A: $i,B: $i] :
( ( class_Groups_Osgn__if @ B )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).
thf(2395,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__field @ D )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(539,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(2908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
thf(1443,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1193,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
thf(5000,plain,
class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
thf(2659,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C )
= A ) )
& ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(690,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
thf(3417,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
thf(2527,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(577,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).
thf(3040,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(550,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).
thf(2947,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
thf(2248,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(567,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
thf(3012,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(3,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
thf(1205,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(287,axiom,
class_Groups_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
thf(2099,plain,
class_Groups_Omonoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= A )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
thf(1591,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= A )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(718,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ A @ D ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__epsilon) ).
thf(3498,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ A @ D ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(365,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
thf(2380,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(125,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
thf(1533,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1068,axiom,
class_Orderings_Oord @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
thf(4614,plain,
class_Orderings_Oord @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(683,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).
thf(3402,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(1042,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__iff) ).
thf(4543,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(1005,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
thf(4403,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(906,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
thf(4090,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1077,axiom,
( ( hAPP @ c_Transcendental_Oarctan @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__zero__zero) ).
thf(4647,plain,
( ( hAPP @ c_Transcendental_Oarctan @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(945,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__mono) ).
thf(4220,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(40,axiom,
class_Rings_Olinordered__semidom @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
thf(1275,plain,
class_Rings_Olinordered__semidom @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
class_Groups_Oab__semigroup__mult @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
thf(1233,plain,
class_Groups_Oab__semigroup__mult @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1145,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
thf(4856,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(897,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
thf(4058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(689,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ! [E: $i] : ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ B @ E @ A )
=> ( ( hAPP @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ B @ D ) @ ( hAPP @ B @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__const__average) ).
thf(3414,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ! [E: $i] : ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ B @ E @ A )
=> ( ( hAPP @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ B @ D ) @ ( hAPP @ B @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(435,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__0__iff) ).
thf(2580,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(536,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Rings_Olinordered__idom @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).
thf(2901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Rings_Olinordered__idom @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
thf(2042,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(1117,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(4762,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(948,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
thf(4234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocomm__monoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).
thf(1671,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(579,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
thf(3049,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(789,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
thf(3745,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(1053,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(4575,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__mult @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(53,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1310,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1074,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(4638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
thf(2712,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(61,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
thf(1327,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(1051,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
thf(4564,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1919,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(822,axiom,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
thf(3826,plain,
class_Groups_Osgn__if @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
thf(1222,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ouminus @ B )
=> ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(778,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
thf(3717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(356,axiom,
class_Rings_Olinordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
thf(2360,plain,
class_Rings_Olinordered__idom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(673,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(3370,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(892,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
thf(4047,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(599,axiom,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
thf(3103,plain,
! [A: $i] :
( ( class_Groups_Ogroup__add @ A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(987,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(4343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(669,axiom,
! [A: $i] :
( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__eq) ).
thf(3350,plain,
! [A: $i] :
( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(877,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
thf(3994,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1032,axiom,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
thf(4496,plain,
class_Int_Onumber__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).
thf(2020,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(801,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).
thf(3777,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1921,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(653,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
thf(3281,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(847,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(3898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
thf(1724,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(1366,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1116,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
thf(4760,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
thf(2405,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(525,axiom,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
thf(2869,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(1125,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
thf(4792,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Omonoid__mult @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
thf(1835,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(643,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
thf(3249,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(996,axiom,
class_Fields_Ofield @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
thf(4371,plain,
class_Fields_Ofield @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber @ C )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= A )
<=> ( A
= ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__reorient) ).
thf(2010,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber @ C )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= A )
=> ( A
= ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) )
& ( ( A
= ( c_Int_Onumber__class_Onumber__of @ C @ B ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(1129,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
thf(4803,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(918,axiom,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
thf(4124,plain,
class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(531,axiom,
class_Rings_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
thf(2886,plain,
class_Rings_Oring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(1162,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(4916,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(1084,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(4665,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(980,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(4322,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(841,axiom,
! [A: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__eq__one__iff) ).
thf(3878,plain,
! [A: $i] :
( ( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
thf(1904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(1067,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= A )
=> ( ( hAPP @ c_Transcendental_Oln @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__unique) ).
thf(4610,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= A )
=> ( ( hAPP @ c_Transcendental_Oln @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
thf(1703,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(17,axiom,
class_Int_Onumber @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
thf(1228,plain,
class_Int_Onumber @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
thf(1482,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(743,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_RealVector_Oreal__normed__field @ C )
& ( class_SEQ_Obanach @ C ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ B ) ) @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__add) ).
thf(3597,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_RealVector_Oreal__normed__field @ C )
& ( class_SEQ_Obanach @ C ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ B ) ) @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(1038,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(4511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(1201,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).
thf(5024,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__div__algebra @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).
thf(953,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__mono) ).
thf(4249,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
thf(1887,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) )
& ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1043,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(4546,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Power_Opower__class_Opower @ D @ C @ B )
= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
thf(1709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( ( c_Power_Opower__class_Opower @ D @ C @ B )
= ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Power_Opower__class_Opower @ D @ C @ B )
= ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(574,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
thf(3029,plain,
class_Orderings_Olinorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(329,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).
thf(2269,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(738,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
thf(3574,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(820,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).
thf(3821,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(833,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
thf(3845,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(534,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
thf(2897,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(670,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(3353,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(1118,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(4766,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(432,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__1__iff) ).
thf(2571,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(844,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_da____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I1_J) ).
thf(3891,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_da____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(1073,axiom,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
thf(4637,plain,
class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(950,axiom,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
thf(4238,plain,
class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(628,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(3204,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(440,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
thf(2603,plain,
class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).
thf(2328,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(758,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(3644,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).
thf(2698,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
= ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
thf(1760,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(605,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
thf(3131,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(1176,axiom,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
thf(4956,plain,
class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1093,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
thf(4692,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(770,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
thf(3689,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(241,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
thf(1907,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
thf(2501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(1080,axiom,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
thf(4654,plain,
class_Fields_Olinordered__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(63,axiom,
class_Rings_Olinordered__semiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
thf(1330,plain,
class_Rings_Olinordered__semiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(2444,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Int_Osucc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).
thf(1264,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Int_Osucc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(748,axiom,
class_Rings_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
thf(3612,plain,
class_Rings_Osemiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(3148,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(761,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
thf(3653,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(331,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
thf(2274,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(713,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).
thf(3485,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(921,axiom,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
thf(4130,plain,
class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(55,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
thf(1313,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(831,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(3840,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
thf(1319,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).
thf(1609,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(978,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
thf(4317,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__squared__eq) ).
thf(2158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(560,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(2989,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(1025,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
thf(4471,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__ring__1 @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(597,axiom,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
thf(3099,plain,
class_Rings_Oordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
thf(1800,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(521,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(2857,plain,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(990,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
thf(4353,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(936,axiom,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
thf(4194,plain,
class_Orderings_Olinorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(2552,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1030,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
thf(4492,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
<=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) )
& ( ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(3216,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(960,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(4270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1046,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
thf(4551,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(137,axiom,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
thf(1568,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(568,axiom,
class_Int_Onumber @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
thf(3014,plain,
class_Int_Onumber @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(1174,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
thf(4952,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(270,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(2024,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(828,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(3835,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1199,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
thf(5020,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).
thf(1004,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls ) @ A )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).
thf(4400,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls ) @ A )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(1875,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
thf(1778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ouminus @ D )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1039,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
thf(4514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(839,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).
thf(3866,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(21,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1232,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(648,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
thf(3268,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(883,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
thf(4008,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).
thf(3258,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1002,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
thf(4396,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(694,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
thf(3431,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1056,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
thf(4583,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
thf(2650,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(773,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( c_Int_Oiszero @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
thf(3702,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( c_Int_Oiszero @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(1132,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(4815,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(223,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
thf(1828,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(497,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
thf(2777,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(45,axiom,
class_Rings_Oordered__comm__semiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
thf(1283,plain,
class_Rings_Oordered__comm__semiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(2017,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(551,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2950,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(1187,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
thf(4988,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(1158,axiom,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
thf(4903,plain,
class_Groups_Oab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(1054,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
= ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
thf(4578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
= ( c_Power_Opower__class_Opower @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1202,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
thf(5027,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(678,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).
thf(3393,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(955,axiom,
class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
thf(4258,plain,
class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
thf(1373,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1064,axiom,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
thf(4600,plain,
class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(499,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
thf(2782,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(765,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
thf(3670,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(1106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
thf(4733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(700,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
thf(3453,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(395,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__square__minus__le) ).
thf(2451,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
thf(1682,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
thf(4847,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(927,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
thf(4147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( A
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_NthRoot_Osqrt @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__real__sqrt__generic) ).
thf(2122,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( A
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_NthRoot_Osqrt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(736,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).
thf(3569,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(854,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
thf(3923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(1127,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
thf(4798,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(917,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
thf(4115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
thf(1581,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(1130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
thf(4810,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(834,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
thf(3851,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
thf(2618,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(2861,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(776,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).
thf(3712,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ D @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(862,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
thf(3955,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(662,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(3327,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2103,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(506,axiom,
class_Rings_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
thf(2804,plain,
class_Rings_Osemiring__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(26,axiom,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_Opred @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).
thf(1242,plain,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_Opred @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(621,axiom,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
thf(3184,plain,
class_Rings_Ono__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(723,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(3510,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(873,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
thf(3986,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
thf(2058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
thf(2437,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(732,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
thf(3537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ( B
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(993,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__pos) ).
thf(4364,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(904,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
thf(4087,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(385,axiom,
! [A: $i] :
( ( ( c_Int_OBit0 @ A )
= c_Int_OPls )
<=> ( A = c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
thf(2424,plain,
! [A: $i] :
( ( ( ( c_Int_OBit0 @ A )
= c_Int_OPls )
=> ( A = c_Int_OPls ) )
& ( ( A = c_Int_OPls )
=> ( ( c_Int_OBit0 @ A )
= c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
thf(2371,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(4996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(611,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ring__1__class_Opower__minus__even) ).
thf(3157,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(973,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
thf(4307,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(766,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(3676,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
thf(1345,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cong) ).
thf(2799,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(637,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
thf(3226,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(254,axiom,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
thf(1943,plain,
class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(631,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
thf(3211,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(370,axiom,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
thf(2392,plain,
class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
thf(2154,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oab__group__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(1058,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
thf(4588,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).
thf(1604,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(540,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
thf(2910,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( c_Int_OBit0 @ B )
!= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
thf(1306,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit0 @ B )
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(730,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(3531,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(1048,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
thf(4557,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(995,axiom,
class_Power_Opower @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
thf(4370,plain,
class_Power_Opower @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(453,axiom,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
thf(2641,plain,
class_Rings_Oordered__ring__abs @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
thf(4925,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(553,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
thf(2954,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
| ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(165,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
thf(1651,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).
thf(4853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(739,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(3582,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(638,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(3229,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(566,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
thf(3011,plain,
class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(4,axiom,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Int_Osucc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit1) ).
thf(1206,plain,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ ( c_Int_Osucc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1066,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
thf(4604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(1197,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
thf(5012,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
& ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).
thf(699,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
thf(3450,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(939,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(4199,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(703,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__one) ).
thf(3459,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(1007,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
<=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
thf(4407,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) )
=> ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( C = A )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(402,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
thf(2473,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(871,axiom,
class_Groups_Oone @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
thf(3984,plain,
class_Groups_Oone @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(647,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
thf(3265,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oab__group__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(1311,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(798,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
thf(3767,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(338,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
thf(2307,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(889,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
thf(4031,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
thf(1736,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(412,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
thf(2496,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
thf(2621,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(975,axiom,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
thf(4312,plain,
class_Groups_Ogroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(931,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
thf(4172,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(1192,axiom,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
thf(4999,plain,
class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(576,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).
thf(3037,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(783,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__zero) ).
thf(3735,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
thf(2409,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(823,axiom,
class_Groups_Ozero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
thf(3827,plain,
class_Groups_Ozero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(424,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
thf(2541,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
thf(1519,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(1217,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(747,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
thf(3610,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__semidom @ B )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(874,axiom,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
thf(3989,plain,
class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(629,axiom,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
thf(3207,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(39,axiom,
class_Groups_Ozero @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
thf(1274,plain,
class_Groups_Ozero @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(390,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
thf(2441,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
thf(2673,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(646,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(3261,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(4712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(482,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
thf(2733,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(69,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
thf(1343,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(885,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(4016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
thf(2805,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
thf(1255,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(998,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(4375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(1013,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
thf(4434,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) ) )
& ( ( ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( B = A ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(941,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
thf(4204,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( c_Power_Opower__class_Opower @ D @ C @ B )
= ( c_Power_Opower__class_Opower @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
thf(2937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( ( c_Power_Opower__class_Opower @ D @ C @ B )
= ( c_Power_Opower__class_Opower @ D @ A @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
=> ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(1034,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_m____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).
thf(4499,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_m____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
thf(2606,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(966,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
thf(4284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(155,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
thf(1619,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(1134,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
thf(4821,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(817,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__inverse) ).
thf(3814,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(559,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2986,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
thf(1423,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(925,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(4140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(895,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).
thf(4053,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ B ) @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
thf(2200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1 @ F )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ B ) @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(310,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(608,axiom,
class_Rings_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
thf(3144,plain,
class_Rings_Oidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(213,axiom,
! [A: $i] :
( ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).
thf(1787,plain,
! [A: $i] :
( ( ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(686,axiom,
! [A: $i,B: $i] :
( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
thf(3408,plain,
! [A: $i,B: $i] :
( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(495,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
thf(2769,plain,
class_Int_Onumber @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(614,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(3166,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(971,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( D != C )
& ( B != A ) )
<=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
thf(4295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
=> ( ( ( ( D != C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ B ) ) ) )
& ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) )
!= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
thf(2464,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(252,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).
thf(1938,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(964,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_da____ @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I3_J) ).
thf(4280,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_da____ @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
thf(2758,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(935,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
thf(4192,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
thf(2670,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(593,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
thf(3090,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
thf(3198,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
= ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(347,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
thf(2332,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
thf(4947,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(791,axiom,
! [A: $i] :
( ( ( class_RealVector_Oreal__normed__field @ A )
& ( class_SEQ_Obanach @ A ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__zero) ).
thf(3750,plain,
! [A: $i] :
( ( ( class_RealVector_Oreal__normed__field @ A )
& ( class_SEQ_Obanach @ A ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
thf(1296,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Oboolean__algebra @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(840,axiom,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
thf(3877,plain,
class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(744,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
thf(3600,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
& ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
thf(1687,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(104,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(1457,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
thf(1819,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(982,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
thf(4327,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(157,axiom,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).
thf(1624,plain,
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1184,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
thf(4979,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(1656,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1008,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
thf(4417,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(856,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
thf(3926,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(316,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
<=> ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
thf(2211,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(1407,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
thf(2547,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(340,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
thf(2313,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(410,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).
thf(2492,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(912,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
thf(4104,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(781,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
thf(3727,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
thf(2741,plain,
! [A: $i,B: $i] :
( ( ( class_Power_Opower @ B )
& ( class_Rings_Osemiring__0 @ B ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(1022,axiom,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
thf(4461,plain,
class_Rings_Osemiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(764,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).
thf(3667,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
| ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1105,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
thf(4732,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(759,axiom,
! [A: $i] :
( ( c_Int_OBit1 @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
thf(3647,plain,
! [A: $i] :
( ( c_Int_OBit1 @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(901,axiom,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
thf(4080,plain,
class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(1088,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ D ) @ B ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).
thf(4680,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ! [D: $i] :
( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ D ) @ B ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(812,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__gt__one) ).
thf(3799,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(1402,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(804,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(3784,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(1177,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_Transcendental_Oln @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inverse) ).
thf(4957,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_Transcendental_Oln @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(304,axiom,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
thf(2157,plain,
class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).
thf(1772,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
thf(1794,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield__inverse__zero @ B )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Int_Oring__char__0 @ B ) )
=> ~ ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).
thf(1328,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Int_Oring__char__0 @ B ) )
=> ~ ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(774,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
<=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).
thf(3704,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(478,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2724,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(1156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
thf(4883,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(760,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(3650,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(452,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
thf(2638,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(866,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
thf(3968,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
thf(1350,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(413,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
thf(2498,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
thf(1234,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(711,axiom,
! [A: $i] : ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oarctan @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__arctan) ).
thf(3482,plain,
! [A: $i] : ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oarctan @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
thf(2515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(288,axiom,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
thf(2100,plain,
class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(688,axiom,
class_Groups_Osgn__if @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
thf(3413,plain,
class_Groups_Osgn__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(1028,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
thf(4486,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(914,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(4108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(355,axiom,
class_Groups_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
thf(2359,plain,
class_Groups_Oab__group__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(81,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(1375,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(472,axiom,
! [A: $i] :
( ( ( class_Fields_Ofield @ A )
& ( class_Int_Onumber__ring @ A ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__numeral__1) ).
thf(2709,plain,
! [A: $i] :
( ( ( class_Fields_Ofield @ A )
& ( class_Int_Onumber__ring @ A ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(16,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
thf(1227,plain,
class_Groups_Ocomm__monoid__mult @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(635,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(3218,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1124,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
thf(4789,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oab__semigroup__idem__mult @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(467,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
thf(2692,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(851,axiom,
? [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096) ).
thf(3916,plain,
? [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
& ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
thf(1755,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
= ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(617,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
thf(3176,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(592,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(3087,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(570,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
thf(3018,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(979,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
thf(4320,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(893,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
thf(4049,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(853,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3922,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1011,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
thf(4425,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(777,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).
thf(3714,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(1114,axiom,
~ ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(4750,plain,
~ ! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
thf(1414,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
thf(2349,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
thf(1446,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(733,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).
thf(3555,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
= ( c_Groups_Oabs__class_Oabs @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(196,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
thf(1744,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(800,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
thf(3775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(607,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
thf(3141,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(528,axiom,
class_Groups_Ozero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
thf(2877,plain,
class_Groups_Ozero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(563,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
thf(3000,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(343,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(2323,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(619,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
thf(3179,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(47,axiom,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
thf(1292,plain,
! [A: $i] :
( c_Int_OPls
!= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(751,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
thf(3622,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(685,axiom,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
thf(3407,plain,
class_Rings_Ocomm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(1120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
thf(4772,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(1006,axiom,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
thf(4406,plain,
class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1111,axiom,
class_Rings_Osemiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
thf(4744,plain,
class_Rings_Osemiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oab__semigroup__add @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(251,axiom,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
thf(1937,plain,
class_Rings_Olinordered__semidom @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1147,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
thf(4861,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(2172,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(693,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(3428,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1149,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__one__iff) ).
thf(4867,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1014,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I2_J) ).
thf(4444,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
thf(2666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C )
= A )
=> ( B
= ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(1612,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(401,axiom,
class_Groups_Ozero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
thf(2472,plain,
class_Groups_Ozero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(33,axiom,
class_Groups_Omonoid__mult @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
thf(1263,plain,
class_Groups_Omonoid__mult @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(544,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
thf(2932,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
!= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
thf(1249,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(408,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
thf(2487,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(788,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cos__x__y__le__one) ).
thf(3743,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
thf(1552,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(250,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__le__one__iff) ).
thf(1932,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(601,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).
thf(3115,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Power_Opower @ C )
& ( class_Rings_Omult__zero @ C )
& ( class_Rings_Ono__zero__divisors @ C )
& ( class_Rings_Ozero__neq__one @ C ) )
=> ( ( ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(186,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(1715,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(852,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
thf(3920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ A @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
thf(3083,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ A @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).
thf(1825,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(555,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
thf(2968,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
!= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(59,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ~ ( c_Int_Oiszero @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).
thf(1324,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ~ ( c_Int_Oiszero @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(603,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(3126,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
thf(2681,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( C
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(805,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
thf(3787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__ring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
thf(1530,plain,
! [A: $i,B: $i] :
( ( class_Power_Opower @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
thf(1539,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(514,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).
thf(2836,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
& ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(535,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(2900,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(20,axiom,
class_Orderings_Opreorder @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
thf(1231,plain,
class_Orderings_Opreorder @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(799,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).
thf(3770,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
thf(2505,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(819,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
thf(3819,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(949,axiom,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
thf(4237,plain,
class_Groups_Omonoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(1169,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
thf(4934,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(1041,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
thf(4540,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield__inverse__zero @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(859,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
thf(3937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
thf(4717,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(988,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(4347,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
thf(1852,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(509,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
thf(2813,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(865,axiom,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
thf(3967,plain,
class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(924,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
<=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ A ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
thf(4135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ A ) @ D ) ) )
& ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ A ) @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
= ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
thf(2766,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(771,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(3692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(406,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(2482,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1157,axiom,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
thf(4902,plain,
class_Orderings_Opreorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(468,axiom,
class_Rings_Oordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
thf(2697,plain,
class_Rings_Oordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(28,axiom,
! [A: $i] :
( ( c_Int_Opred @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Int_Opred @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit0) ).
thf(1246,plain,
! [A: $i] :
( ( c_Int_Opred @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Int_Opred @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(582,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
thf(3064,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(956,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__less__iff) ).
thf(4259,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(586,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
thf(3074,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(1092,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
thf(4689,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(2203,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(753,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(3624,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(835,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
thf(3856,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(658,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
thf(3306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(879,axiom,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
thf(3999,plain,
class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(153,axiom,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
thf(1616,plain,
class_Rings_Ocomm__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(1190,axiom,
class_Int_Onumber @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
thf(4995,plain,
class_Int_Onumber @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).
thf(1045,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
thf(4550,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).
thf(2749,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
thf(1434,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).
thf(1991,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(501,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
thf(2788,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(425,axiom,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
thf(2546,plain,
class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(937,axiom,
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
thf(4195,plain,
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).
thf(2208,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__vector @ B )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(902,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
thf(4081,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(652,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
thf(3279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(741,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
thf(3587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1179,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
thf(4966,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
thf(1695,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(1160,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(4906,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(389,axiom,
class_Orderings_Oord @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
thf(2440,plain,
class_Orderings_Oord @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(377,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
thf(2408,plain,
class_Int_Onumber__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(624,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(3190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
= ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).
thf(1515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Olinordered__field @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(891,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).
thf(4036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(2729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(762,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ge__zero) ).
thf(3660,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(922,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one0) ).
thf(4131,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(1090,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
thf(4685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(1698,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1151,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_d____ ) @ v_m____ ) @ v_e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dm_I2_J) ).
thf(4874,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_d____ ) @ v_m____ ) @ v_e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(588,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
thf(3079,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1050,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
thf(4562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(808,axiom,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
thf(3792,plain,
class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(650,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Power_Opower__class_Opower @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).
thf(3274,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Power_Opower__class_Opower @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(769,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
thf(3686,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(772,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
thf(3696,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(1019,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
thf(4453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Osemiring @ E )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1164,axiom,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
thf(4921,plain,
class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( c_Int_OBit1 @ B )
!= ( c_Int_OBit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
thf(1278,plain,
! [A: $i,B: $i] :
( ( c_Int_OBit1 @ B )
!= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1163,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(4919,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(2413,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(1150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
thf(4872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(537,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_Osucc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).
thf(2904,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_Osucc @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(578,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(3042,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(436,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
thf(2585,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(475,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oln @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ln) ).
thf(2717,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oln @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(9,axiom,
class_Rings_Ocomm__semiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
thf(1219,plain,
class_Rings_Ocomm__semiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(746,axiom,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
thf(3607,plain,
! [A: $i,B: $i] :
( ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
| ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
thf(1548,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(1927,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(872,axiom,
class_SEQ_Obanach @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__SEQ_Obanach) ).
thf(3985,plain,
class_SEQ_Obanach @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(785,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(3738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(985,axiom,
class_Orderings_Oorder @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
thf(4340,plain,
class_Orderings_Oorder @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(843,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
thf(3888,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(830,axiom,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
thf(3839,plain,
class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(727,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
thf(3523,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(926,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__divide__inverse) ).
thf(4144,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
thf(1916,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(720,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
thf(3504,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(211,axiom,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
thf(1784,plain,
class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(929,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
thf(4159,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(558,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
thf(2981,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(707,axiom,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).
thf(3472,plain,
! [A: $i] :
( ( class_Groups_Osgn__if @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ C @ B ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
thf(2393,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ C @ B ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(1087,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
thf(4677,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(1099,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
thf(4709,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(1024,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hAPP @ c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__eq__zero__iff) ).
thf(4465,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( hAPP @ c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ c_Transcendental_Oln @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
thf(1535,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(702,axiom,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
thf(3458,plain,
class_Rings_Olinordered__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(2398,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(745,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
thf(3604,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
thf(1965,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(1059,axiom,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
thf(4590,plain,
class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(2134,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(632,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(3213,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(880,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__cancel) ).
thf(4000,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(676,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
thf(3387,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(623,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
thf(3187,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(787,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
thf(3741,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1083,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) @ A )
= ( c_Int_OBit0 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).
thf(4662,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) @ A )
= ( c_Int_OBit0 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(986,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
thf(4341,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(959,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__real__sqrt__sumsq) ).
thf(4268,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(584,axiom,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
thf(3070,plain,
class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(757,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
thf(3636,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(855,axiom,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
thf(3925,plain,
class_Int_Oring__char__0 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(816,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
thf(3811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(502,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
thf(2791,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(795,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
thf(3758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
thf(1929,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(15,axiom,
class_Orderings_Olinorder @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
thf(1226,plain,
class_Orderings_Olinorder @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(1488,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(810,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(3796,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(571,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
thf(3023,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(909,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
thf(4096,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(38,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Int_Opred @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit1) ).
thf(1271,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Int_Opred @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(915,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_d____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I1_J) ).
thf(4112,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_d____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(663,axiom,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
thf(3330,plain,
class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
<=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) )
& ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ C )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(490,axiom,
class_Groups_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
thf(2753,plain,
class_Groups_Omonoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(803,axiom,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
thf(3783,plain,
class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(898,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
thf(4060,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
thf(2557,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(657,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).
thf(3304,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
thf(1464,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(13,axiom,
class_Groups_Oone @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
thf(1224,plain,
class_Groups_Oone @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
thf(1675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
thf(2161,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(954,axiom,
! [A: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
= A )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln__iff) ).
thf(4251,plain,
! [A: $i] :
( ( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
= A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(864,axiom,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oln @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__exp) ).
thf(3964,plain,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oln @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
thf(1635,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(545,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
thf(2935,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).
thf(1733,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add__abs @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1052,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
thf(4573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(24,axiom,
class_Groups_Omonoid__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
thf(1239,plain,
class_Groups_Omonoid__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
thf(1332,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(602,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).
thf(3123,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(827,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__cancel__iff) ).
thf(3832,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(203,axiom,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
thf(1765,plain,
class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(750,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Power_Opower__class_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).
thf(3619,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( ( c_Power_Opower__class_Opower @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(961,axiom,
class_Groups_Ouminus @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
thf(4273,plain,
class_Groups_Ouminus @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
thf(1258,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1012,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
thf(4433,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
thf(1356,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(2148,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(779,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__minus) ).
thf(3719,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(878,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
thf(3996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(1096,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__iff) ).
thf(4699,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(675,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
thf(3384,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1001,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
thf(4388,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
thf(2346,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(767,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
thf(3678,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(283,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_Osucc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).
thf(2079,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_Osucc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(357,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
thf(2361,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(5,axiom,
! [A: $i] :
( ( c_Int_Opred @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).
thf(1209,plain,
! [A: $i] :
( ( c_Int_Opred @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
thf(2721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__not__eq__zero) ).
thf(2119,plain,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(984,axiom,
! [A: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__minus) ).
thf(4337,plain,
! [A: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(1097,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(4704,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(44,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
thf(1282,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(2478,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
thf(2151,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(454,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
thf(2642,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(366,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
= ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
thf(2383,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
= ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(2624,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(797,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
thf(3764,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(381,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
thf(2415,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(768,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).
thf(3683,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(725,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
thf(3515,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(325,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).
thf(2257,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) )
& ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(143,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(1589,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(323,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(2246,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
thf(2299,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(1065,axiom,
! [A: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__inverse) ).
thf(4601,plain,
! [A: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(600,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).
thf(3106,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(705,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
thf(3468,plain,
class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(1057,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
thf(4586,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(2839,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(206,axiom,
class_Rings_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
thf(1771,plain,
class_Rings_Omult__zero @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(548,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
thf(2943,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(775,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
thf(3710,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(549,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(2945,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1085,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
thf(4667,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
thf(3138,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(179,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
thf(1690,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
thf(3182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(526,axiom,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).
thf(2871,plain,
! [A: $i] :
( ( class_RealVector_Oreal__normed__algebra__1 @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A )
<=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
thf(1376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1036,axiom,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
thf(4509,plain,
class_Rings_Omult__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(1027,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) )
<=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
thf(4477,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oidom @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) )
=> ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
& ( ( ( B = A )
| ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
thf(3160,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(512,axiom,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__def) ).
thf(2824,plain,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A )
= B ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(790,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
thf(3747,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Olemma__DERIV__subst) ).
thf(2632,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( B = A )
=> ( c_Deriv_Oderiv @ E @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(1023,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
thf(4462,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ C ) @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(1133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
thf(4818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(957,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
thf(4264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F ) @ E ) @ D )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(868,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
thf(3977,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(70,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
thf(1344,plain,
class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(837,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__iff) ).
thf(3861,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(1189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
thf(4993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(557,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(2974,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1047,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
thf(4554,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(1015,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_d____ @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I2_J) ).
thf(4445,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_d____ @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(1339,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1009,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
thf(4420,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(1155,axiom,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
thf(4882,plain,
class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1136,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__self) ).
thf(4833,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(498,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__half__sum) ).
thf(2780,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(2267,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(888,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(4028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Ocomm__semiring__1 @ E )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(737,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
thf(3572,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1186,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(4985,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).
thf(392,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
thf(2446,plain,
class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(963,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
thf(4277,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(613,axiom,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
thf(3165,plain,
class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(932,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
thf(4181,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(500,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
thf(2785,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
thf(4850,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(565,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).
thf(3006,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls ) ) ) ) )
& ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls ) ) ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(656,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
thf(3298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1079,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(4652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(527,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
thf(2874,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(1460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(334,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
thf(2289,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber @ B )
& ( class_Rings_Odivision__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide__number__of) ).
thf(2647,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber @ B )
& ( class_Rings_Odivision__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1089,axiom,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
thf(4684,plain,
class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(516,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
thf(2842,plain,
class_Int_Oring__char__0 @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(2365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(755,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(3627,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
thf(1528,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(284,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(2086,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(815,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
thf(3806,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(333,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
thf(2288,plain,
class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(640,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
thf(3241,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
!= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(496,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
<=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
thf(2770,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) ) )
& ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(383,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
thf(2418,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(1140,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
thf(4844,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(1103,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
thf(4720,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
thf(1841,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
thf(1396,plain,
! [A: $i,B: $i] :
( ( class_Fields_Ofield @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
thf(2725,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(374,axiom,
! [A: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ A )
& ( class_Int_Onumber__ring @ A ) )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Rings_Oinverse__class_Odivide @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half) ).
thf(2401,plain,
! [A: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ A )
& ( class_Int_Onumber__ring @ A ) )
=> ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Rings_Oinverse__class_Odivide @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
thf(1594,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(7,axiom,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
thf(1213,plain,
! [A: $i] :
( ( c_Int_OBit1 @ A )
!= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(829,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
thf(3838,plain,
class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(513,axiom,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
thf(2835,plain,
class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(277,axiom,
! [A: $i] :
( ( c_Int_OPls
= ( c_Int_OBit0 @ A ) )
<=> ( c_Int_OPls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
thf(2051,plain,
! [A: $i] :
( ( ( c_Int_OPls
= ( c_Int_OBit0 @ A ) )
=> ( c_Int_OPls = A ) )
& ( ( c_Int_OPls = A )
=> ( c_Int_OPls
= ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(692,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
thf(3423,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ A @ C ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
thf(2550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ A @ C ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(27,axiom,
class_Orderings_Oord @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
thf(1245,plain,
class_Orderings_Oord @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).
thf(2369,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(992,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
thf(4362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__semiring__strict @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(322,axiom,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
thf(2244,plain,
( c_Int_OPls
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(489,axiom,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
thf(2752,plain,
class_Rings_Ozero__neq__one @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(289,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(2101,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(972,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(4304,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(190,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1726,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
thf(4954,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(369,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
thf(2390,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(724,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).
thf(3512,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1033,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
thf(4497,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__ring @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(899,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).
thf(4067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(314,axiom,
class_Rings_Omult__zero @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
thf(2207,plain,
class_Rings_Omult__zero @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(716,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).
thf(3490,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(903,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
thf(4084,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(943,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
<=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
thf(4207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) )
=> ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B = A )
| ( C
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ B )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1110,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__real__def) ).
thf(4741,plain,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(552,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).
thf(2952,plain,
( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
thf(2096,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1021,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
thf(4458,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__idom @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
thf(4813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Olinordered__idom @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(400,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(2471,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(2037,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(42,axiom,
class_Rings_Osemiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
thf(1277,plain,
class_Rings_Osemiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1055,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
thf(4581,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(133,axiom,
c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos2) ).
thf(1551,plain,
c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Oboolean__algebra @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(90,axiom,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
thf(1413,plain,
class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(541,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
thf(2914,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(510,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
thf(2816,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
thf(1873,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(625,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
thf(3193,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ A @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
thf(1758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ A @ B ) @ ( c_Power_Opower__class_Opower @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
thf(2318,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(680,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
thf(3395,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
thf(2271,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(1020,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ B ) @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).
thf(4456,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ B ) @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1107,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
thf(4735,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(870,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
thf(3981,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(529,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
thf(2878,plain,
class_Orderings_Oorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(970,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
thf(4292,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(394,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(2449,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oabs__if @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).
thf(2927,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oabs__if @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Oabs__class_Oabs @ B @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(449,axiom,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
thf(2629,plain,
! [A: $i,B: $i] :
( ( ( class_Fields_Ofield @ B )
& ( class_Int_Onumber__ring @ B ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).
thf(4859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
thf(2684,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(701,axiom,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
thf(3455,plain,
! [A: $i] :
( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
thf(1472,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(518,axiom,
( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
thf(2846,plain,
( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(916,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(4113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(431,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(2564,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
thf(1845,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( A
!= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
thf(1748,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(784,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3737,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(474,axiom,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
thf(2715,plain,
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(660,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(3315,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1148,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
thf(4864,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(589,axiom,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
thf(3082,plain,
class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(633,axiom,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( c_Int_Oiszero @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).
thf(3214,plain,
! [A: $i] :
( ( class_Rings_Osemiring__1 @ A )
=> ( c_Int_Oiszero @ A @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(1165,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
thf(4922,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(1061,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
thf(4593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1198,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__cmult__Id) ).
thf(5018,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( c_Deriv_Oderiv @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(1170,axiom,
! [A: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
thf(4937,plain,
! [A: $i] :
( ( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).
thf(2375,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) )
& ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(14,axiom,
class_Groups_Ocomm__monoid__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
thf(1225,plain,
class_Groups_Ocomm__monoid__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(195,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__one) ).
thf(1743,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(300,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
thf(2143,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(849,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
thf(3904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
thf(2588,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(793,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
thf(3754,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(1173,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
thf(4950,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
thf(1368,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1075,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__le__cancel__iff) ).
thf(4641,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(968,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
thf(4287,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(511,axiom,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
thf(2821,plain,
! [A: $i] :
( ( class_Fields_Ofield__inverse__zero @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
= ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(630,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(3209,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(35,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
thf(1267,plain,
class_Rings_Oordered__cancel__semiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(3058,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(367,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).
thf(2386,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(19,axiom,
class_Rings_Ono__zero__divisors @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
thf(1230,plain,
class_Rings_Ono__zero__divisors @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(520,axiom,
! [A: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
thf(2850,plain,
! [A: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(642,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).
thf(3246,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(1003,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ B ) @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__monotone) ).
thf(4398,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ B ) @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(542,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(2920,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(780,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__exp__iff) ).
thf(3722,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(667,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
thf(3344,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(946,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
thf(4222,plain,
! [A: $i,B: $i] :
( ( class_Rings_Omult__zero @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(821,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ B ) @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
thf(3823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Rings_Olinordered__semiring__1__strict @ F )
=> ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
=> ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
= ( c_Groups_Oone__class_Oone @ F ) )
=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ B ) @ E ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(595,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(3095,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(1152,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
thf(4875,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
thf(2354,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).
thf(2656,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1 @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( c_Groups_Oone__class_Oone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( c_Deriv_Oderiv @ B @ ( c_Transcendental_Oexp @ B ) @ A @ ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__exp) ).
thf(2747,plain,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( c_Deriv_Oderiv @ B @ ( c_Transcendental_Oexp @ B ) @ A @ ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(115,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
thf(1499,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(697,axiom,
class_Rings_Osemiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
thf(3448,plain,
class_Rings_Osemiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(977,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
thf(4314,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_RealVector_Oreal__normed__algebra @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(934,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
thf(4190,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(308,axiom,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_Osucc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).
thf(2165,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_Osucc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(842,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
thf(3885,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
thf(1813,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ A )
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
thf(1300,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(1452,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(649,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(3273,plain,
c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(665,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
thf(3334,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(708,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
thf(3475,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(573,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
thf(3026,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(1203,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
thf(5030,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).
thf(813,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__def) ).
thf(3801,plain,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(57,axiom,
( ( c_Int_Osucc @ c_Int_OPls )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Pls) ).
thf(1317,plain,
( ( c_Int_Osucc @ c_Int_OPls )
= ( c_Int_OBit1 @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
thf(1763,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(989,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
thf(4351,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber @ C )
& ( class_Orderings_Olinorder @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
<=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber @ C )
& ( class_Orderings_Olinorder @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(824,axiom,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
thf(3828,plain,
class_Rings_Oordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(923,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
thf(4132,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__algebra @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).
thf(1658,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(128,axiom,
class_Rings_Oordered__semiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
thf(1538,plain,
class_Rings_Oordered__semiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1194,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
thf(5001,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
thf(2701,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1128,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
thf(4800,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(1185,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
thf(4982,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(752,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(3623,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(616,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
thf(3174,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(1108,axiom,
class_Rings_Oring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
thf(4737,plain,
class_Rings_Oring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(399,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__exp__le__zero) ).
thf(2468,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(10,axiom,
class_Rings_Oordered__semiring @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
thf(1220,plain,
class_Rings_Oordered__semiring @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(561,axiom,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
thf(2992,plain,
class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(216,axiom,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__real__def) ).
thf(1802,plain,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(952,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(4246,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(434,axiom,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
thf(2579,plain,
class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
thf(3224,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(940,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
thf(4202,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(1094,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).
thf(4695,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ B @ D ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(907,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_d____ ) @ v_m____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dm_I1_J) ).
thf(4093,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_d____ ) @ v_m____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
thf(3071,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Int_Onumber @ D )
& ( class_Rings_Osemiring @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1126,axiom,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
thf(4795,plain,
! [A: $i,B: $i] :
( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(928,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
thf(4150,plain,
! [A: $i,B: $i] :
( ( class_Rings_Oring__1__no__zero__divisors @ B )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
& ( ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
| ( A
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(654,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Int_Oring__char__0 @ B ) )
=> ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) )
<=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).
thf(3288,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Int_Oring__char__0 @ B ) )
=> ( ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
& ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
thf(1404,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
thf(1358,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(379,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero) ).
thf(2411,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(714,axiom,
class_Rings_Oring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
thf(3488,plain,
class_Rings_Oring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(131,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
thf(1543,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).
thf(1766,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).
thf(1898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Ofield__inverse__zero @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(31,axiom,
class_Rings_Osemiring__1 @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
thf(1257,plain,
class_Rings_Osemiring__1 @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(867,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
thf(3970,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
& ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
thf(2113,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ C )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
= ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(825,axiom,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
thf(3829,plain,
class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1071,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
thf(4624,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C ) @ A ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1183,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
thf(4976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(11,axiom,
class_Groups_Oab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
thf(1221,plain,
class_Groups_Oab__semigroup__add @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1029,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
thf(4488,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
=> ( ( E
!= ( c_Groups_Ozero__class_Ozero @ F ) )
=> ( ( ( D = C )
& ( B != A ) )
=> ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ E ) @ B ) )
!= ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OBit1 @ B )
= ( c_Int_OBit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
thf(1284,plain,
! [A: $i,B: $i] :
( ( ( ( c_Int_OBit1 @ B )
= ( c_Int_OBit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Int_OBit1 @ B )
= ( c_Int_OBit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(74,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__inv__sqrt__pow2) ).
thf(1353,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1037,axiom,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
thf(4510,plain,
class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(1113,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__le__mono) ).
thf(4748,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
thf(2843,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
thf(1485,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__unique) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_RealVector_Oreal__normed__field @ E )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ B )
=> ( ( c_Deriv_Oderiv @ E @ D @ C @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(913,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
thf(4106,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(1188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
thf(4991,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).
thf(117,axiom,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
thf(1506,plain,
! [A: $i] :
( ( class_Rings_Odivision__ring @ A )
=> ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(480,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
thf(2728,plain,
class_Orderings_Opreorder @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(958,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
thf(4267,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(947,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
thf(4225,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__no__zero__divisors @ C )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1138,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
thf(4838,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(533,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
thf(2892,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(726,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(3520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(2848,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(25,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Code__Numeral_Ocode__numeral )
= ( c_Int_Onumber__class_Onumber__of @ tc_Code__Numeral_Ocode__numeral @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).
thf(1240,plain,
( ( c_Groups_Oone__class_Oone @ tc_Code__Numeral_Ocode__numeral )
= ( c_Int_Onumber__class_Onumber__of @ tc_Code__Numeral_Ocode__numeral @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(944,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
thf(4217,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(709,axiom,
class_Power_Opower @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
thf(3478,plain,
class_Power_Opower @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(794,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
thf(3757,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(583,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(3067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(1119,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
thf(4770,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
thf(1685,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(339,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
thf(2310,plain,
! [A: $i,B: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(89,axiom,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
thf(1412,plain,
class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).
thf(1781,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Fields_Ofield @ E )
=> ( ( D
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ E ) )
=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
= ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ A ) @ D ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ A @ C ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Power_Opower__class_Opower @ D @ A @ C ) @ ( c_Power_Opower__class_Opower @ D @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(524,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
thf(2865,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
| ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__field @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(861,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
thf(3946,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(969,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
thf(4289,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
thf(2626,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
= ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(1095,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_em0) ).
thf(4698,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(742,axiom,
! [A: $i,B: $i] :
( ( ( c_Int_OBit0 @ B )
= ( c_Int_OBit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
thf(3589,plain,
! [A: $i,B: $i] :
( ( ( ( c_Int_OBit0 @ B )
= ( c_Int_OBit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Int_OBit0 @ B )
= ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(981,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(4325,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( class_Groups_Omonoid__mult @ B )
& ( class_Int_Onumber @ B ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
thf(2045,plain,
! [A: $i,B: $i] :
( ( ( class_Groups_Omonoid__mult @ B )
& ( class_Int_Onumber @ B ) )
=> ( ( c_Power_Opower__class_Opower @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(594,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
thf(3092,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(1171,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
thf(4944,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
thf(1913,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1082,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
thf(4656,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ C )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(1049,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
thf(4559,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
thf(4738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
thf(1517,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(344,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
thf(2325,plain,
! [A: $i] :
( ( class_Rings_Olinordered__idom @ A )
=> ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(857,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
thf(3928,plain,
class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1076,axiom,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
thf(4646,plain,
class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(900,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(4078,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
thf(2110,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ocomm__monoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(661,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(3320,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
thf(2071,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(858,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
thf(3929,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(974,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
thf(4310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(538,axiom,
class_Groups_Oone @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
thf(2907,plain,
class_Groups_Oone @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(41,axiom,
class_Rings_Osemiring__0 @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
thf(1276,plain,
class_Rings_Osemiring__0 @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
thf(1646,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(60,axiom,
class_Rings_Omult__zero @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
thf(1326,plain,
class_Rings_Omult__zero @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(749,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Int_Oring__char__0 @ C ) )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).
thf(3613,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Int_Oring__char__0 @ C ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(368,axiom,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
thf(2389,plain,
class_Rings_Osemiring__0 @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(712,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
thf(3484,plain,
class_Power_Opower @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1069,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(4615,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_RealVector_Oreal__normed__field @ C )
& ( class_SEQ_Obanach @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ B ) ) @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ A ) )
= ( hAPP @ ( c_Transcendental_Oexp @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__exp__exp) ).
thf(2554,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_RealVector_Oreal__normed__field @ C )
& ( class_SEQ_Obanach @ C ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ B ) ) @ ( hAPP @ ( c_Transcendental_Oexp @ C ) @ A ) )
= ( hAPP @ ( c_Transcendental_Oexp @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
thf(2532,plain,
! [A: $i,B: $i] :
( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(920,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(4126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(197,axiom,
! [A: $i] :
( ( c_Int_OBit0 @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
thf(1745,plain,
! [A: $i] :
( ( c_Int_OBit0 @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(556,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
thf(2971,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(386,axiom,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).
thf(2431,plain,
! [A: $i] :
( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(591,axiom,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
thf(3085,plain,
( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(838,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
thf(3864,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
thf(2594,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
=> ( ( ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( B
= ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Rings_Olinordered__idom @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i] :
( ( ( class_Int_Onumber__ring @ C )
& ( class_Rings_Olinordered__idom @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(172,axiom,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
thf(1674,plain,
class_Groups_Oab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(806,axiom,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
thf(3789,plain,
class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(163,axiom,
! [A: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
thf(1639,plain,
! [A: $i] :
( ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
=> ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
thf(4715,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Oordered__comm__semiring @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
thf(1629,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(876,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
thf(3991,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(271,axiom,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).
thf(2026,plain,
! [A: $i] :
( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
& ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
=> ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
= ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(756,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
thf(3630,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ogroup__add @ B )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(719,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(3501,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
thf(3003,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
thf(2764,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__ab__group__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(220,axiom,
class_Rings_Olinordered__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
thf(1822,plain,
class_Rings_Olinordered__ring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1031,axiom,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
thf(4495,plain,
class_Rings_Odivision__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(1098,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= A )
=> ( ( hAPP @ c_Transcendental_Oln @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ln__eq) ).
thf(4705,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B )
= A )
=> ( ( hAPP @ c_Transcendental_Oln @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(836,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
thf(3859,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Rings_Oordered__semiring @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ D ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E @ C ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(664,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_Opred @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__pred) ).
thf(3331,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_Opred @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(672,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
thf(3368,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(644,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
thf(3252,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring__inverse__zero @ B )
=> ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(1135,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(4823,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(1180,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(4969,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ B ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).
thf(763,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
<=> ( c_Int_Oiszero @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).
thf(3662,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
=> ( c_Int_Oiszero @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) )
& ( ( c_Int_Oiszero @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
= ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(802,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
thf(3780,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
thf(2796,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Omonoid__mult @ D )
=> ( ( c_Power_Opower__class_Opower @ D @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1121,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
thf(4774,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(184,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(1706,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
thf(1607,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).
thf(1661,plain,
! [A: $i,B: $i] :
( ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1016,axiom,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
thf(4446,plain,
class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(1112,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__exp__less__zero) ).
thf(4745,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(393,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__ge__add__one__self__aux) ).
thf(2447,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(403,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
thf(2475,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__add @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(1144,axiom,
class_Rings_Oidom @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
thf(4855,plain,
class_Rings_Oidom @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(938,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
thf(4197,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1078,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
thf(4649,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ono__zero__divisors @ C )
=> ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(740,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
thf(3585,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(1060,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
thf(4591,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
thf(1440,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1200,axiom,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
thf(5023,plain,
class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).
thf(1000,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_d____ @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I3_J) ).
thf(4387,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_d____ @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ v_e @ v_m____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Power_Opower__class_Opower @ tc_Int_Oint @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
thf(2576,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Power_Opower__class_Opower @ tc_Int_Oint @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(809,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
thf(3793,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(6,axiom,
class_Power_Opower @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
thf(1212,plain,
class_Power_Opower @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
thf(1893,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).
thf(2294,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Int_Onumber__ring @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
thf(2739,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(910,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
thf(4098,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
thf(2494,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(997,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
<=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
thf(4372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(796,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
thf(3761,plain,
! [A: $i,B: $i] :
( ( class_Rings_Odivision__ring @ B )
=> ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
= ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1167,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(4927,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(887,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(4025,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(1070,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
thf(4619,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(691,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_four__x__squared) ).
thf(3420,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
= ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(152,axiom,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
thf(1614,plain,
( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
thf(2421,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Int_Onumber__ring @ D )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(674,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
thf(3379,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(919,axiom,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
thf(4125,plain,
class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(290,axiom,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
thf(2102,plain,
class_Groups_Omonoid__mult @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(1512,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1086,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ B )
= ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
thf(4670,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_NthRoot_Osqrt @ B )
= ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_NthRoot_Osqrt @ B )
= ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(476,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__add__one__self__le__self) ).
thf(2719,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(18,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
thf(1229,plain,
class_Rings_Ocomm__semiring__1 @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(598,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
thf(3100,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(276,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(2050,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(717,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(3496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
thf(1480,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Olinordered__field @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1063,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
thf(4597,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
=> ( B
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(994,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero__iff) ).
thf(4367,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(706,axiom,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oarctan @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__half) ).
thf(3469,plain,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oarctan @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( hAPP @ c_Transcendental_Oarctan @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(363,axiom,
class_Groups_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
thf(2374,plain,
class_Groups_Ogroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(1154,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
thf(4880,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(1196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
thf(5009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
thf(2517,plain,
! [A: $i,B: $i] :
( ( class_Groups_Olinordered__ab__group__add @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(884,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
thf(4014,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semiring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1091,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
thf(4687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semiring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(999,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(4378,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(639,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(3232,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(655,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A )
<=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
thf(3291,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B ) )
& ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
= B )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(991,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(4356,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(850,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring__abs @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
| ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
thf(3907,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__ring__abs @ C )
=> ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
| ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(1195,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__exp__iff) ).
thf(5004,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).
thf(782,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oln @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__ln__divide) ).
thf(3733,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_Transcendental_Oln @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(1062,axiom,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
thf(4596,plain,
class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(845,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
thf(3892,plain,
! [A: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
thf(2736,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__semidom @ C )
=> ( ( ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1123,axiom,
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).
thf(4787,plain,
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1139,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
thf(4841,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(807,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
thf(3790,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(171,axiom,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
thf(1673,plain,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
<=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).
thf(3015,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ B ) ) @ ( c_Power_Opower__class_Opower @ tc_Int_Oint @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1115,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__less__cancel__iff) ).
thf(4755,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ B ) @ ( hAPP @ ( c_Transcendental_Oexp @ tc_RealDef_Oreal ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(734,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
<=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
thf(3558,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__idom @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
!= ( c_Groups_Ozero__class_Ozero @ C ) )
| ( A
!= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Power_Opower__class_Opower @ C @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ C @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1026,axiom,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__divide) ).
thf(4474,plain,
! [A: $i,B: $i] :
( ( hAPP @ c_NthRoot_Osqrt @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ B ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(486,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
thf(2746,plain,
class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).
thf(1335,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(626,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(3196,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
thf(2223,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(2340,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(659,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( c_Int_Oiszero @ B @ A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).
thf(3309,plain,
! [A: $i,B: $i] :
( ( class_Rings_Osemiring__1 @ B )
=> ( ( ( c_Int_Oiszero @ B @ A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( c_Int_Oiszero @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(609,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
thf(3145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__semidom @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Power_Opower__class_Opower @ D @ C @ B ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
thf(2636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(846,axiom,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
thf(3897,plain,
class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1122,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
thf(4777,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(894,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(4051,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(77,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
thf(1363,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Oone__class_Oone @ A )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(56,axiom,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).
thf(1314,plain,
! [A: $i] :
( ( c_Int_Osucc @ ( c_Int_OBit0 @ A ) )
= ( c_Int_OBit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(965,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__le__cancel__iff) ).
thf(4281,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ B ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(668,axiom,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
thf(3347,plain,
! [A: $i,B: $i] :
( ( ( class_Int_Onumber__ring @ B )
& ( class_Rings_Olinordered__idom @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(967,axiom,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
thf(4286,plain,
class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(651,axiom,
( ( c_Groups_Ozero__class_Ozero @ tc_Code__Numeral_Ocode__numeral )
= ( c_Int_Onumber__class_Onumber__of @ tc_Code__Numeral_Ocode__numeral @ c_Int_OPls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).
thf(3277,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Code__Numeral_Ocode__numeral )
= ( c_Int_Onumber__class_Onumber__of @ tc_Code__Numeral_Ocode__numeral @ c_Int_OPls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(618,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ C ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__less) ).
thf(3177,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ C ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ C @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(814,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
thf(3804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ B ) @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(710,axiom,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ B @ ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exp__minus) ).
thf(3479,plain,
! [A: $i,B: $i] :
( ( ( class_RealVector_Oreal__normed__field @ B )
& ( class_SEQ_Obanach @ B ) )
=> ( ( hAPP @ ( c_Transcendental_Oexp @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
= ( c_Rings_Oinverse__class_Oinverse @ B @ ( hAPP @ ( c_Transcendental_Oexp @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(382,axiom,
class_Rings_Osemiring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
thf(2417,plain,
class_Rings_Osemiring @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(575,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).
thf(3030,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ozero @ B )
=> ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
= A )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ B ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Ozero__class_Ozero @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(890,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
thf(4034,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(721,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
thf(3506,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Ocancel__ab__semigroup__add @ D )
=> ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
= ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(832,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__gt__zero) ).
thf(3843,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(641,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
thf(3244,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(321,axiom,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
thf(2241,plain,
! [A: $i] :
( ( class_Int_Onumber__ring @ A )
=> ( ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
thf(2810,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) )
= ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(604,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(3128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Ocomm__semiring__1 @ D )
=> ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
= ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(572,axiom,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
thf(3025,plain,
class_Rings_Ozero__neq__one @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(505,axiom,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
thf(2803,plain,
class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(671,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
thf(3360,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ C ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ C ) ) )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
= ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(398,axiom,
class_Groups_Omonoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
thf(2467,plain,
class_Groups_Omonoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(1976,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(715,axiom,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
thf(3489,plain,
c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(818,axiom,
( ( hAPP @ c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__one) ).
thf(3817,plain,
( ( hAPP @ c_Transcendental_Oln @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(677,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
thf(3392,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(942,axiom,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
thf(4206,plain,
class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(554,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
thf(2966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(36,axiom,
class_Rings_Ozero__neq__one @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
thf(1268,plain,
class_Rings_Ozero__neq__one @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(439,axiom,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
thf(2600,plain,
! [A: $i] :
( ( class_Rings_Ozero__neq__one @ A )
=> ( ( c_Groups_Ozero__class_Ozero @ A )
!= ( c_Groups_Oone__class_Oone @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(687,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_NthRoot_Osqrt @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__real__sqrt) ).
thf(3411,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( c_Deriv_Oderiv @ tc_RealDef_Oreal @ c_NthRoot_Osqrt @ A @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(127,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
thf(1537,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1181,axiom,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_da____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d1_I2_J) ).
thf(4972,plain,
c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_da____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(951,axiom,
! [A: $i] :
( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
thf(4239,plain,
! [A: $i] :
( ( ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
=> ( ( hAPP @ c_NthRoot_Osqrt @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(417,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
thf(2507,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(983,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(4330,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(860,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
thf(3939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Olinordered__ring__strict @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
& ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
| ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
& ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ B ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(465,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ A )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sqrt__divide__self__eq) ).
thf(2687,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ A )
= ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(523,axiom,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
thf(2864,plain,
class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(786,axiom,
class_Groups_Oabs__if @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
thf(3740,plain,
class_Groups_Oabs__if @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
<=> ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Odivision__ring @ D )
=> ( ( C
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A )
=> ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) ) )
& ( ( B
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ C ) )
=> ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(886,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( hAPP @ c_Transcendental_Oln @ B )
= ( hAPP @ c_Transcendental_Oln @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__inj__iff) ).
thf(4019,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( ( ( hAPP @ c_Transcendental_Oln @ B )
= ( hAPP @ c_Transcendental_Oln @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Transcendental_Oln @ B )
= ( hAPP @ c_Transcendental_Oln @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(49,axiom,
class_Rings_Olinordered__semiring__strict @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
thf(1299,plain,
class_Rings_Olinordered__semiring__strict @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(587,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).
thf(3076,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Odivision__ring @ C )
=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
= ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(679,axiom,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
thf(3394,plain,
class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(1399,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Ocomm__semiring__1 @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).
thf(1621,plain,
! [A: $i,B: $i] :
( ( class_RealVector_Oreal__normed__field @ B )
=> ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(905,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__gt__zero) ).
thf(4088,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ c_Transcendental_Oln @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Opred @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).
thf(2138,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Opred @ B ) @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Opred @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(666,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(3341,plain,
! [A: $i,B: $i] :
( ( class_Rings_Ocomm__semiring__1 @ B )
=> ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(696,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
thf(3437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(704,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
<=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
thf(3461,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
=> ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
& ( ( A
= ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
=> ( B
= ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(962,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
thf(4274,plain,
! [A: $i,B: $i,C: $i] :
( ( class_RealVector_Oreal__normed__algebra @ C )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
thf(1944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Ofield__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
& ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
!= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
= B ) )
& ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
= ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( C
= ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
=> ( C
= ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(754,axiom,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
thf(3626,plain,
class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
thf(2690,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Oordered__comm__monoid__add @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(930,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).
thf(4161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Fields_Olinordered__field__inverse__zero @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ A ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(1044,axiom,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oarctan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arctan__minus) ).
thf(4547,plain,
! [A: $i] :
( ( hAPP @ c_Transcendental_Oarctan @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
= ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oarctan @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(228,axiom,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
thf(1848,plain,
! [A: $i] :
( ( class_Rings_Olinordered__semidom @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(242,axiom,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
thf(1912,plain,
class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oring__1 @ C )
=> ( ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Power_Opower__class_Opower @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(792,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
thf(3753,plain,
class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(1040,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
<=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
thf(4533,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Olinordered__ring__strict @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
& ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
| ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(848,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
thf(3901,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(728,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
thf(3526,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(64,axiom,
class_Orderings_Oorder @ tc_Code__Numeral_Ocode__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
thf(1331,plain,
class_Orderings_Oorder @ tc_Code__Numeral_Ocode__numeral,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(148,axiom,
class_Groups_Ouminus @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
thf(1606,plain,
class_Groups_Ouminus @ tc_Int_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(729,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).
thf(3528,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Fields_Ofield__inverse__zero @ C )
=> ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Power_Opower__class_Opower @ C @ B @ A ) )
= ( c_Power_Opower__class_Opower @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(491,axiom,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
thf(2754,plain,
! [A: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
!= ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(1081,axiom,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
thf(4655,plain,
class_Rings_Oring__1 @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(530,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
<=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).
thf(2879,plain,
! [A: $i,B: $i] :
( ( class_Groups_Oone @ B )
=> ( ( ( ( c_Groups_Oone__class_Oone @ B )
= A )
=> ( A
= ( c_Groups_Oone__class_Oone @ B ) ) )
& ( ( A
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( ( c_Groups_Oone__class_Oone @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(1072,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(4627,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Groups_Ogroup__add @ C )
=> ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
<=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).
thf(2887,plain,
! [A: $i,B: $i] :
( ( class_Int_Onumber__ring @ B )
=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) )
=> ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) )
& ( ( c_Int_Oiszero @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
=> ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
= ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(684,axiom,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
thf(3405,plain,
( ( c_Int_OBit0 @ c_Int_OPls )
= c_Int_OPls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(281,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__pow2) ).
thf(2074,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal @ ( hAPP @ c_NthRoot_Osqrt @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) )
<=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
thf(1490,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) )
=> ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(336,axiom,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
thf(2297,plain,
! [A: $i,B: $i] :
( ( class_Fields_Olinordered__field @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(976,axiom,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
thf(4313,plain,
class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).
thf(2615,plain,
! [A: $i,B: $i] :
( ( class_Rings_Olinordered__idom @ B )
=> ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
=> ( ( c_Groups_Osgn__class_Osgn @ B @ A )
= ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
thf(1769,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1010,axiom,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ln__less__zero) ).
thf(4423,plain,
! [A: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ c_Transcendental_Oln @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
<=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
& ( class_Int_Onumber @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
& ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(896,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
thf(4056,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Rings_Oordered__cancel__semiring @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
thf(2993,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
=> ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
= ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1,conjecture,
c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_da____ ) @ v_m____ ) @ v_e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_da____ ) @ v_m____ ) @ v_e ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1204,plain,
~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ v_da____ ) @ v_m____ ) @ v_e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).
thf(1449,plain,
! [A: $i,B: $i] :
( ( class_Groups_Omonoid__mult @ B )
=> ( ( c_Power_Opower__class_Opower @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
= ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(292,axiom,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
thf(2106,plain,
class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(457,axiom,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
thf(2655,plain,
class_Rings_Olinordered__semidom @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(881,axiom,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
thf(4002,plain,
! [A: $i] :
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(5033,plain,
$false,
inference(e,[status(thm)],[2163,1665,1586,4909,1633,3399,3798,4729,3434,3397,3449,2331,3566,4877,4447,3962,1337,1718,2612,4094,1469,4835,1823,4450,4005,3053,4101,4183,3979,3830,1850,2480,1982,4904,3172,3185,3990,2512,1924,4500,3509,3098,4960,1269,4973,1305,1437,2363,2077,3534,4931,2940,1596,2395,2908,1443,5000,2659,3417,2527,3040,2947,2248,3012,1205,2099,1591,3498,2380,1533,4614,3402,4543,4403,4090,4647,4220,1275,1233,4856,4058,3414,2580,2901,2042,4762,4234,1671,3049,3745,4575,1310,4638,2434,2712,1327,4564,1919,3826,1222,3717,2360,3370,4047,3103,4343,3350,3994,4496,2020,3777,1921,3281,3898,1724,1366,4760,2405,2869,4792,1835,3249,4371,2010,4803,4124,2886,4916,4665,4322,3878,1904,4610,1703,1228,1482,3597,4511,5024,4249,1887,4546,1709,3029,2269,3574,3821,1455,3845,2897,3353,4766,2571,2703,3891,4637,4238,3204,2603,2328,1430,3644,2698,1760,3131,4956,4692,3689,1907,2501,4654,1330,2444,1264,3612,3148,3653,2274,3485,4130,1313,3840,2403,1319,1609,4317,2158,2989,4471,3099,1800,2857,4353,4194,2552,4492,1347,3216,4270,4551,1568,3014,2520,4952,2024,3835,5020,4400,1875,1778,4514,3866,1232,3268,4008,3258,4396,3431,4583,2650,3702,4815,1828,2777,1283,2017,2950,4988,4903,4578,5027,3393,4258,1373,4600,2782,3670,4733,3453,2451,1682,4847,4147,2122,3569,1677,3923,4798,4115,1581,4810,3851,2618,2861,3712,3955,3327,2103,2804,1242,3184,3510,3986,2058,2367,2437,3537,4364,4087,2424,2371,1394,4996,3157,4307,3676,1345,2799,3226,1943,3211,2392,2154,4588,1604,2910,1306,3531,4557,4370,2641,4925,2954,1651,4853,3582,3229,3011,1206,4604,5012,3450,4199,3459,4407,2473,3984,3265,1311,3767,2307,4031,1736,2496,2621,4312,4172,4999,1730,3037,3735,2409,3827,2541,1519,2277,1570,1217,3610,3989,3207,1274,2441,2673,3261,4712,2733,1343,4016,2805,1255,4375,4434,4204,2937,4499,2606,4284,1619,4821,3814,2986,1423,4140,4053,2200,2179,3144,1787,3408,2769,3166,4295,2464,1938,4280,2758,4192,2670,3090,3198,1555,2332,4947,3750,1296,3877,3600,1687,1457,1819,4327,1624,4979,1656,4417,3926,2211,1407,2547,2313,2492,4104,3727,2741,4461,2228,3667,4732,3647,4080,4680,3799,1402,3784,4957,2157,1772,1794,1328,3704,2724,4883,3650,2638,3968,1350,2498,1234,1541,3482,2515,2100,3413,4486,4108,2359,1375,2709,1227,3218,4789,2692,1587,3916,1755,3176,3087,3018,4320,4049,3922,4425,3714,4750,1414,2349,1446,3555,1744,3775,3141,2877,3000,2323,3179,1292,3622,3407,4772,4406,1584,4744,1700,1937,4861,2172,3428,4867,4444,2666,1612,2472,1263,2932,1249,2487,3743,1552,1932,3115,1715,3920,3083,1825,2968,1324,3126,2681,3787,1530,1539,2836,2900,1231,3770,1974,2505,3819,4237,4934,4540,3937,4717,4347,1852,2813,3967,4135,2766,3692,2482,4902,2697,1246,3064,4259,1979,3074,4689,2203,3624,3856,3306,3999,1616,2338,4995,4550,2749,1434,1991,2788,2546,4195,2208,4081,3279,3587,4966,1695,4906,2440,2408,3190,1515,4036,2729,3660,1727,4131,4685,1698,4874,3079,4562,3792,3274,3686,3696,4453,4921,1278,4919,2413,4872,2904,3042,2585,2717,1219,3607,1548,1927,3985,3738,4340,3888,3839,3523,4144,1916,3504,1784,4159,2981,3472,2393,4677,4709,4465,1535,3458,2398,3604,1965,4590,2134,3213,4000,3387,3187,3741,4662,1833,4341,4268,3070,3636,2048,3925,3811,2791,3758,1929,1226,1488,3796,3023,4096,1271,4112,3330,1865,2753,3783,4060,2557,3304,1464,1224,1675,2161,4251,2220,3964,1635,2935,1733,4573,1239,1332,3123,3832,1765,3619,4273,1258,4433,1356,2148,3719,3996,4699,3384,4388,2346,3678,2079,2361,1209,2721,2119,4337,4704,1282,2478,2151,2642,2383,2624,3764,2415,3683,3515,2257,1589,2246,2299,4601,3106,3468,4586,2839,1771,2943,3710,2945,4667,3138,1690,3182,2871,1376,4509,4477,3160,2824,2182,3747,2632,4462,4818,4264,3977,1344,3861,4993,2974,4554,4445,1339,4420,4882,1557,2343,4833,2780,2267,4028,3572,4985,2446,4277,3165,1862,4181,2785,4850,3006,3298,4652,2874,1460,2289,2647,4684,2842,2365,1474,3627,1528,2086,3806,2288,3241,2022,2069,2770,2418,4844,4720,1841,1396,2725,2401,1594,1213,3838,2835,2051,3423,2550,1245,2369,4362,1775,2244,2752,2101,4304,1726,4954,2390,3512,4497,4067,2207,3490,4084,1626,4207,4741,2952,2096,4458,4813,2471,2037,1277,4581,1551,2005,1413,2914,2816,1873,3193,1758,2107,2318,3395,2271,4456,4735,1420,3981,2878,2503,4292,2449,1509,2927,2629,4859,2684,3455,1472,2846,4113,2564,1845,1748,3737,2715,3315,4864,3082,3214,4922,4593,5018,4937,2375,1225,1743,2143,3904,2588,3754,4950,1368,4641,4287,2821,3209,1267,3058,2386,1230,2850,3246,4398,2920,3722,3344,4222,1785,3823,3095,4875,2354,2656,2747,1499,3448,4314,4190,2165,3885,1813,1300,1452,1637,3273,3334,3475,3026,5030,3801,1317,1763,4351,1901,3828,4132,1658,1538,5001,2701,4800,4982,3623,1679,3174,4737,2468,1220,2992,1802,4246,2579,3224,1504,4202,4695,4093,3071,4795,4150,3288,1404,1358,2411,3488,1543,1766,1898,1257,3970,2113,3829,4624,4976,1221,4488,1284,1353,4510,4748,2357,2843,1485,2320,4106,4991,1506,2728,4267,4225,4838,2892,3520,2848,1240,4217,1617,3478,3757,3067,4770,1685,2310,1412,1781,2490,2865,1940,3946,4289,2626,4698,3589,4325,2045,3092,4944,1913,4656,4559,4738,1517,2325,3928,4646,4078,2110,3320,2071,3929,4310,2907,1276,1646,1326,3613,2389,3484,4615,2554,2532,4126,1745,2971,2431,2262,3085,3864,2594,1721,1674,3789,1639,4715,1629,3991,2026,3630,3501,3003,2764,1822,4495,4705,3859,3331,3368,3252,4823,4969,3662,3780,2796,4774,1706,1607,1661,4446,4745,2447,2475,4855,4197,4649,3585,4591,1440,5023,4387,2576,3793,1212,2230,1893,2294,2739,4098,2494,4372,3761,1994,4927,4025,4619,3420,1614,2421,3379,4125,2102,1512,4670,2719,1229,3100,2604,2050,3496,1480,4597,4367,3469,2374,4880,5009,2517,4014,4687,4378,3232,3291,4356,3907,5004,3733,4596,3892,2736,4787,2008,4841,3790,1673,3015,1816,4755,3558,4474,2746,1335,3196,2223,2340,3309,3145,2636,3897,4777,4051,1363,1314,4281,3347,4286,3277,3177,3804,3479,2417,3030,4034,3506,3843,3244,2241,2810,3128,3025,2803,3360,2265,2467,1976,3489,3817,3392,4206,2966,1268,2600,3411,2485,1537,4972,4239,2507,4330,3939,2687,2864,3740,1880,4019,1299,3076,3394,1399,1621,4088,2138,3341,3437,3461,4274,1944,3626,2690,4161,4547,1848,1912,1417,3753,4533,3901,3526,1331,1606,3528,2754,4655,2879,4627,1962,2887,3405,2074,1490,2297,4313,2615,1769,4423,2453,4056,2993,1204,1449,2106,2087,2655,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:44:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.10 % [INFO] Parsing done (262ms).
% 1.94/1.11 % [INFO] Running in sequential loop mode.
% 2.56/1.32 % [INFO] eprover registered as external prover.
% 2.56/1.32 % [INFO] cvc4 registered as external prover.
% 2.56/1.32 % [INFO] Scanning for conjecture ...
% 2.75/1.45 % [INFO] Found a conjecture and 1249 axioms. Running axiom selection ...
% 3.78/1.65 % [INFO] Axiom selection finished. Selected 1201 axioms (removed 48 axioms).
% 5.09/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 5.09/2.03 % [INFO] Type checking passed.
% 5.09/2.03 % [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 ...
% 21.43/5.93 % External prover 'e' found a proof!
% 21.43/5.93 % [INFO] Killing All external provers ...
% 21.43/5.93 % Time passed: 5417ms (effective reasoning time: 4821ms)
% 21.43/5.93 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 21.43/5.94 % Axioms used in derivation (1201): arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1, fact_mult__exp__exp, fact_zero__power2, arity_Int__Oint__Rings_Ocomm__semiring, fact_zle__refl, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_pos2, fact_zero__le__divide__iff, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_xt1_I1_J, fact_less__eq__int__code_I14_J, fact_real__le__refl, fact_real__sqrt__sum__squares__mult__squared__eq, fact_not__sum__power2__lt__zero, arity_fun__Orderings_Oorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_one__code__numeral__code, fact_Numeral1__eq1__nat, fact_power__abs, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, arity_Code____Numeral__Ocode____numeral__Rings_Osemiring, fact_neg__le__divide__eq, fact_power__strict__decreasing, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, arity_RealDef__Oreal__Orderings_Oord, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_DERIV__const__average, fact_arctan__monotone, fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_minus__Bit0, fact_incr__mult__lemma, arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring, fact_lemma__sqrt__hcomplex__capprox, fact_mult__1__left, fact_minus__mult__left, fact_neg__divide__le__eq, fact_inverse__1, fact_mult__less__cancel__left__disj, fact_semiring__norm_I112_J, fact_realpow__two__sum__zero__iff, fact_dm_I2_J, fact_abs__if, fact_bin__less__0__simps_I4_J, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_odd__nonzero, arity_RealDef__Oreal__Groups_Ozero, fact_mult__nonneg__nonpos, 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% 21.43/5.94 % No. of inferences in proof: 2406
% 21.43/5.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5417 ms resp. 4821 ms w/o parsing
% 22.69/6.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.69/6.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------